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<title>LaTeX syntax for mathematics</title>
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<main id="latex-syntax-for-mathematics">
<h1 class="title">LaTeX syntax for mathematics</h1>

<div class="topic abstract" role="doc-abstract">
<p class="topic-title">Abstract</p>
<p>Docutils supports mathematical content with a <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/directives.html#math">&quot;math&quot;
directive</a> and <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/roles.html#math">role</a>. The input format is <em>LaTeX math
syntax</em><a class="brackets" href="#math-syntax" id="footnote-reference-1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> with support for literal Unicode symbols.</p>
</div>
<!-- Minimal menu bar for inclusion in documentation sources
in ``docutils/docs/*/`` sub-sub-diretories.

Attention: this is not a standalone document. -->
<nav class="contents" id="contents" role="doc-toc">
<p class="topic-title">Contents</p>
<ul class="auto-toc simple">
<li><p><a class="reference internal" href="#inline-formulas-and-displayed-equations" id="toc-entry-1"><span class="sectnum">1 </span>Inline formulas and displayed equations</a></p></li>
<li><p><a class="reference internal" href="#mathematical-symbols" id="toc-entry-2"><span class="sectnum">2 </span>Mathematical symbols</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#accents-and-embellishments" id="toc-entry-3"><span class="sectnum">2.1 </span>Accents and embellishments</a></p></li>
<li><p><a class="reference internal" href="#binary-operators" id="toc-entry-4"><span class="sectnum">2.2 </span>Binary operators</a></p></li>
<li><p><a class="reference internal" href="#extensible-delimiters" id="toc-entry-5"><span class="sectnum">2.3 </span>Extensible delimiters</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#pairing-delimiters" id="toc-entry-6"><span class="sectnum">2.3.1 </span>Pairing delimiters</a></p></li>
<li><p><a class="reference internal" href="#nonpairing-delimiters" id="toc-entry-7"><span class="sectnum">2.3.2 </span>Nonpairing delimiters</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#extensible-vertical-arrows" id="toc-entry-8"><span class="sectnum">2.4 </span>Extensible vertical arrows</a></p></li>
<li><p><a class="reference internal" href="#functions-named-operators" id="toc-entry-9"><span class="sectnum">2.5 </span>Functions (named operators)</a></p></li>
<li><p><a class="reference internal" href="#greek-letters" id="toc-entry-10"><span class="sectnum">2.6 </span>Greek letters</a></p></li>
<li><p><a class="reference internal" href="#letterlike-symbols" id="toc-entry-11"><span class="sectnum">2.7 </span>Letterlike symbols</a></p></li>
<li><p><a class="reference internal" href="#math-alphabets" id="toc-entry-12"><span class="sectnum">2.8 </span>Math alphabets</a></p></li>
<li><p><a class="reference internal" href="#miscellaneous-symbols" id="toc-entry-13"><span class="sectnum">2.9 </span>Miscellaneous symbols</a></p></li>
<li><p><a class="reference internal" href="#punctuation" id="toc-entry-14"><span class="sectnum">2.10 </span>Punctuation</a></p></li>
<li><p><a class="reference internal" href="#relation-symbols" id="toc-entry-15"><span class="sectnum">2.11 </span>Relation symbols</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#arrows" id="toc-entry-16"><span class="sectnum">2.11.1 </span>Arrows</a></p></li>
<li><p><a class="reference internal" href="#comparison" id="toc-entry-17"><span class="sectnum">2.11.2 </span>Comparison</a></p></li>
<li><p><a class="reference internal" href="#miscellaneous-relations" id="toc-entry-18"><span class="sectnum">2.11.3 </span>Miscellaneous relations</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#variable-sized-operators" id="toc-entry-19"><span class="sectnum">2.12 </span>Variable-sized operators</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#notations" id="toc-entry-20"><span class="sectnum">3 </span>Notations</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#top-and-bottom-embellishments" id="toc-entry-21"><span class="sectnum">3.1 </span>Top and bottom embellishments</a></p></li>
<li><p><a class="reference internal" href="#extensible-arrows" id="toc-entry-22"><span class="sectnum">3.2 </span>Extensible arrows</a></p></li>
<li><p><a class="reference internal" href="#affixing-symbols-to-other-symbols" id="toc-entry-23"><span class="sectnum">3.3 </span>Affixing symbols to other symbols</a></p></li>
<li><p><a class="reference internal" href="#matrices" id="toc-entry-24"><span class="sectnum">3.4 </span>Matrices</a></p></li>
<li><p><a class="reference internal" href="#spacing-commands" id="toc-entry-25"><span class="sectnum">3.5 </span>Spacing commands</a></p></li>
<li><p><a class="reference internal" href="#modular-arithmetic-and-modulo-operation" id="toc-entry-26"><span class="sectnum">3.6 </span>Modular arithmetic and modulo operation</a></p></li>
<li><p><a class="reference internal" href="#roots" id="toc-entry-27"><span class="sectnum">3.7 </span>Roots</a></p></li>
<li><p><a class="reference internal" href="#boxed-formulas" id="toc-entry-28"><span class="sectnum">3.8 </span>Boxed formulas</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#fractions-and-related-constructions" id="toc-entry-29"><span class="sectnum">4 </span>Fractions and related constructions</a></p></li>
<li><p><a class="reference internal" href="#delimiter-sizes" id="toc-entry-30"><span class="sectnum">5 </span>Delimiter sizes</a></p></li>
<li><p><a class="reference internal" href="#text" id="toc-entry-31"><span class="sectnum">6 </span>Text</a></p></li>
<li><p><a class="reference internal" href="#integrals-and-sums" id="toc-entry-32"><span class="sectnum">7 </span>Integrals and sums</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#altering-the-placement-of-limits" id="toc-entry-33"><span class="sectnum">7.1 </span>Altering the placement of limits</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#changing-the-size-of-elements-in-a-formula" id="toc-entry-34"><span class="sectnum">8 </span>Changing the size of elements in a formula</a></p></li>
</ul>
</nav>
<section id="inline-formulas-and-displayed-equations">
<h2><a class="toc-backref" href="#toc-entry-1" role="doc-backlink"><span class="sectnum">1 </span>Inline formulas and displayed equations</a></h2>
<p>The <strong>math role</strong> can be used for inline mathematical expressions:
<span class="docutils literal"><span class="pre">:math:`\psi(r)</span> = <span class="pre">\exp(-2r)`</span></span> will produce <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&psi;</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo><mi>exp</mi><mo stretchy="false">(</mo><mo>-</mo><mn>2</mn><mi>r</mi><mo stretchy="false">)</mo></mrow></math>.
Inside the backtics you can write anything you would write between dollar
signs in a LaTeX document.  <a class="brackets" href="#math-syntax" id="footnote-reference-2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a></p>
<aside class="admonition tip">
<p class="admonition-title">Tip</p>
<p>If you put <span class="docutils literal">.. <span class="pre">default-role::</span> math</span> at the top of your
document, you can write <span class="docutils literal">`x^2`</span> instead of the longer
version: <span class="docutils literal"><span class="pre">:math:`x^2`</span></span>.  You can also introduce an
abbreviation like this <span class="docutils literal">.. role:: m(math)</span>.  That will allow
you to write <span class="docutils literal"><span class="pre">:m:`x^2`</span></span> or <span class="docutils literal"><span class="pre">`x^2`:m:</span></span>.</p>
</aside>
<p>The <strong>math directive</strong> is used for displayed equations. It corresponds to
an <span class="docutils literal">equation*</span> or <span class="docutils literal">align*</span> environment in a LaTeX document. If you
write:</p>
<pre class="literal-block">.. math:: \psi(r) = e^{-2r}</pre>
<p>you will get:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow><mi mathvariant="italic">&psi;</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo>
<msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo><mn>2</mn><mi>r</mi></mrow>
</msup>
</mrow>
    </mstyle></math>
</div>
<p>A more complex example is the definition of the <a class="reference internal" href="#fourier-transform">Fourier transform</a>:</p>
<pre class="literal-block">.. math::
   :name: Fourier transform

   (\mathcal{F}f)(y)
    = \frac{1}{\sqrt{2\pi}^{\ n}}
      \int_{\mathbb{R}^n} f(x)\,
      e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.</pre>
<p>which is rendered as:</p>
<pre class="math problematic" id="fourier-transform">
  (\mathcal{F}f)(y)
   = \frac{1}{\sqrt{2\pi}^{\ n}}
     \int_{\mathbb{R}^n} f(x)\,
     e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 60)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbb in equation, Line 2.</p>
</aside>
<p>The <span class="docutils literal">:name:</span> option puts a label on the equation that can be
linked to by <a class="reference external" href="../ref/rst/restructuredtext.html#hyperlink-references">hyperlink references</a>.</p>
<p>Displayed equations can use <span class="docutils literal">\\</span> and <span class="docutils literal">&amp;</span> for line shifts and alignments:</p>
<pre class="literal-block">.. math::

 a &amp;= (x + y)^2         &amp;  b &amp;= (x - y)^2 \\
   &amp;= x^2 + 2xy + y^2   &amp;    &amp;= x^2 - 2xy + y^2</pre>
<p>LaTeX output will wrap it in an <span class="docutils literal">align*</span> environment.
The result is:</p>
<pre class="math problematic">
a &amp; = (x + y)^2         &amp;  b &amp; = (x - y)^2 \\
  &amp; = x^2 + 2xy + y^2   &amp;    &amp; = x^2 - 2xy + y^2
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 81)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{align*} Line 1.</p>
</aside>
<p>The <span class="docutils literal">aligned</span> environment can be used as a component in a containing
expression. E.g.,</p>
<pre class="literal-block">.. math::
  \left.
    \begin{aligned}
      B' &amp; = -\partial\times E,         \\
      E' &amp; = \partial\times B - 4\pi j,
    \end{aligned}
  \right\}
  \qquad \text{Maxwell’s equations}</pre>
<p>results in</p>
<pre class="math problematic">
\left.
  \begin{aligned}
    B' &amp; = -\partial\times E         \\
    E' &amp; =  \partial\times B - 4\pi j
  \end{aligned}
\;\right\}
\qquad \text{Maxwell’s equations.}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 100)</p>
<p>'latin-1' codec can't encode character '\u2019' in position 168: ordinal not in range(256)</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="math-syntax" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#footnote-reference-1">1</a>,<a role="doc-backlink" href="#footnote-reference-2">2</a>)</span>
<p>The supported LaTeX commands include AMS extensions
(see, e.g., the <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>). Some of the shown symbols
require the &quot;amssymb&quot; <a class="reference external" href="../../user/latex.html#latex-document-classes-and-packages">LaTeX package</a> (or another package providing
the AMS symbol macros) when exported with the &quot;latex&quot; writer.</p>
<p>The support is limited to a subset of <em>LaTeX math</em> by the conversion
required for many output formats.  For HTML, the <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
configuration setting (or the corresponding <span class="docutils literal"><span class="pre">--math-output</span></span> command
line option) selects between alternative output formats with different
subsets of supported elements. If a writer does not support math
typesetting, the content is inserted verbatim.</p>
</aside>
</aside>
</section>
<section id="mathematical-symbols">
<h2><a class="toc-backref" href="#toc-entry-2" role="doc-backlink"><span class="sectnum">2 </span>Mathematical symbols</a></h2>
<p>The following tables are adapted from the first edition of
&quot;The LaTeX Companion&quot; (Goossens, Mittelbach, Samarin) and the
AMS <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>.</p>
<section id="accents-and-embellishments">
<h3><a class="toc-backref" href="#toc-entry-3" role="doc-backlink"><span class="sectnum">2.1 </span>Accents and embellishments</a></h3>
<p>The &quot;narrow&quot; accents are intended for a single-letter base.</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>\<mo>'</mo><mi>x</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\acute{x}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>t</mi></mrow>
<mo>&middot;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\dot{t}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>\`<mi>x</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\grave{x}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>x</mi></mrow>
<mo>&rarr;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\vec{x}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>v</mi></mrow>
<mo>&OverBar;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\bar{v}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>t</mi></mrow>
<mo>&middot;&middot;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\ddot{t}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>x</mi></mrow>
<mo>&Hat;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\hat{x}</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>x</mi></mrow>
<mo>&breve;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\breve{x}</span></p></td>
<td><p><span class="math problematic">\dddot{t}</span></p></td>
<td><p><span class="docutils literal">\dddot{t}</span></p></td>
<td><p><span class="math problematic">\mathring{x}</span></p></td>
<td><p><span class="docutils literal">\mathring{x}</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>x</mi></mrow>
<mo>&vee;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\check{x}</span></p></td>
<td><p><span class="math problematic">\ddddot{t}</span></p></td>
<td><p><span class="docutils literal">\ddddot{t}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi>n</mi></mrow>
<mo>~</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\tilde{n}</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 150)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \dddot in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 150)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathring in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 151)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ddddot in equation, Line 1.</p>
</aside>
<p>When adding an accent to an i or j in math, dotless variants can be
obtained with <span class="docutils literal">\imath</span> and <span class="docutils literal">\jmath</span>: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi mathvariant="italic">&imath;</mi></mrow>
<mo>&Hat;</mo></mover>
</mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi mathvariant="italic">&jmath;</mi></mrow>
<mo>&rarr;</mo></mover>
</mrow></math>.</p>
<p>For embellishments that span multiple symbols, use:</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&tilde;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\widetilde{gbi}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&Hat;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\widehat{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&OverBar;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\overline{gbi}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<munder><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&OverBar;</mo></munder>
</mrow></math></p></td>
<td><p><span class="docutils literal">\underline{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow>
<mover><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&OverBrace;</mo></mover>
</mrow>
</mrow></math></p></td>
<td><p><span class="docutils literal">\overbrace{gbi}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow>
<munder><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&UnderBrace;</mo></munder>
</mrow>
</mrow></math></p></td>
<td><p><span class="docutils literal">\underbrace{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&leftarrow;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\overleftarrow{gbi}</span></p></td>
<td><p><span class="math problematic">\underleftarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\underleftarrow{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mover><mrow><mi mathvariant="italic">gbi</mi></mrow>
<mo stretchy="true">&rightarrow;</mo></mover>
</mrow></math></p></td>
<td><p><span class="docutils literal">\overrightarrow{gbi}</span></p></td>
<td><p><span class="math problematic">\underrightarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\underrightarrow{gbi}</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\overleftrightarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\overleftrightarrow{gbi}</span></p></td>
<td><p><span class="math problematic">\underleftrightarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\underleftrightarrow{gbi}</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
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</aside>
<aside class="system-message">
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<p class="pre-wrap">Unknown command \overleftrightarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
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</aside>
</section>
<section id="binary-operators">
<h3><a class="toc-backref" href="#toc-entry-4" role="doc-backlink"><span class="sectnum">2.2 </span>Binary operators</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>*</mo></mrow></math></p></td>
<td><p><span class="docutils literal">*</span></p></td>
<td><p><span class="math problematic">\circledast</span></p></td>
<td><p><span class="docutils literal">\circledast</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ominus;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\ominus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>+</mo></mrow></math></p></td>
<td><p><span class="docutils literal">+</span></p></td>
<td><p><span class="math problematic">\circledcirc</span></p></td>
<td><p><span class="docutils literal">\circledcirc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&oplus;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\oplus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>-</mo></mrow></math></p></td>
<td><p><span class="docutils literal">-</span></p></td>
<td><p><span class="math problematic">\circleddash</span></p></td>
<td><p><span class="docutils literal">\circleddash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&oslash;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\oslash</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>:</mo></mrow></math></p></td>
<td><p><span class="docutils literal">:</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&cup;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\cup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&otimes;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\otimes</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\Cap</span></p></td>
<td><p><span class="docutils literal">\Cap</span></p></td>
<td><p><span class="math problematic">\curlyvee</span></p></td>
<td><p><span class="docutils literal">\curlyvee</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&PlusMinus;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\pm</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\Cup</span></p></td>
<td><p><span class="docutils literal">\Cup</span></p></td>
<td><p><span class="math problematic">\curlywedge</span></p></td>
<td><p><span class="docutils literal">\curlywedge</span></p></td>
<td><p><span class="math problematic">\rightthreetimes</span></p></td>
<td><p><span class="docutils literal">\rightthreetimes</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&amalg;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\amalg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&dagger;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\dagger</span></p></td>
<td><p><span class="math problematic">\rtimes</span></p></td>
<td><p><span class="docutils literal">\rtimes</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ast;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\ast</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ddagger;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\ddagger</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&setminus;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\setminus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigcirc;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\bigcirc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&loz;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\diamond</span></p></td>
<td><p><span class="math problematic">\smallsetminus</span></p></td>
<td><p><span class="docutils literal">\smallsetminus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigtriangledown;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\bigtriangledown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&divide;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\div</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sqcap;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sqcap</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigtriangleup;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\bigtriangleup</span></p></td>
<td><p><span class="math problematic">\divideontimes</span></p></td>
<td><p><span class="docutils literal">\divideontimes</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sqcup;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sqcup</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\boxdot</span></p></td>
<td><p><span class="docutils literal">\boxdot</span></p></td>
<td><p><span class="math problematic">\dotplus</span></p></td>
<td><p><span class="docutils literal">\dotplus</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&star;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\star</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\boxminus</span></p></td>
<td><p><span class="docutils literal">\boxminus</span></p></td>
<td><p><span class="math problematic">\doublebarwedge</span></p></td>
<td><p><span class="docutils literal">\doublebarwedge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&times;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\times</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\boxplus</span></p></td>
<td><p><span class="docutils literal">\boxplus</span></p></td>
<td><p><span class="math problematic">\gtrdot</span></p></td>
<td><p><span class="docutils literal">\gtrdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&triangleleft;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\triangleleft</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\boxtimes</span></p></td>
<td><p><span class="docutils literal">\boxtimes</span></p></td>
<td><p><span class="math problematic">\intercal</span></p></td>
<td><p><span class="docutils literal">\intercal</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&triangleright;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\triangleright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bullet;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\bullet</span></p></td>
<td><p><span class="math problematic">\leftthreetimes</span></p></td>
<td><p><span class="docutils literal">\leftthreetimes</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&uplus;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\uplus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&cap;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\cap</span></p></td>
<td><p><span class="math problematic">\lessdot</span></p></td>
<td><p><span class="docutils literal">\lessdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&vee;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\vee</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&middot;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\cdot</span></p></td>
<td><p><span class="math problematic">\ltimes</span></p></td>
<td><p><span class="docutils literal">\ltimes</span></p></td>
<td><p><span class="math problematic">\veebar</span></p></td>
<td><p><span class="docutils literal">\veebar</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\centerdot</span></p></td>
<td><p><span class="docutils literal">\centerdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&mp;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\mp</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&and;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\wedge</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&SmallCircle;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\circ</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&odot;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\odot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&wr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\wr</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 176)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circledast in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 177)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circledcirc in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 178)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circleddash in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Cap in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \curlyvee in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Cup in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \curlywedge in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 181)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \rightthreetimes in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 182)</p>
<p>TeX to MathML converter `ttm` failed:</p>
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</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \smallsetminus in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \divideontimes in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \boxdot in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \dotplus in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \doublebarwedge in equation, Line 1.</p>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \boxplus in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gtrdot in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \boxtimes in equation, Line 1.</p>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \intercal in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leftthreetimes in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lessdot in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 193)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ltimes in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \veebar in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \centerdot in equation, Line 1.</p>
</aside>
</section>
<section id="extensible-delimiters">
<h3><a class="toc-backref" href="#toc-entry-5" role="doc-backlink"><span class="sectnum">2.3 </span>Extensible delimiters</a></h3>
<p>Unless you indicate otherwise, delimiters in math formulas remain at the
standard size regardless of the height of the enclosed material. To get
adaptable sizes, use <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> prefixes, for example
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>g</mi><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>X</mi><mo>=</mo>
<msup><mrow><mi>h</mi></mrow><mrow><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">]</mo></mrow>
</msup>
<mo stretchy="false">(</mo><mi>Y</mi><mo stretchy="false">)</mo><mo>)</mo></mrow></mrow></math> or</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow>
<msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow>
</msub>
<mo>=</mo>
<msup><mrow><mo>(</mo>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mn>2</mn></mrow>
</mfrac>
<mo>)</mo></mrow><mrow><mi>n</mi></mrow>
</msup>
</mrow>
    </mstyle></math>
</div>
<p>Use <span class="docutils literal">.</span> for &quot;empty&quot; delimiters:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow><mi>A</mi><mo>=</mo>
<msubsup><mrow><mo> </mo>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mn>1</mn><mo>-</mo><mi>n</mi></mrow>
</mfrac>
<mi>&ensp;</mi><mo>|</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn> </mrow>
<mrow><mi mathvariant="italic">&infin;</mi></mrow></msubsup>
</mrow>
    </mstyle></math>
</div>
<p>See also the commands for fixed <a class="reference internal" href="#delimiter-sizes">delimiter sizes</a> below.</p>
<p>The following symbols extend when used with <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span>:</p>
<section id="pairing-delimiters">
<h4><a class="toc-backref" href="#toc-entry-6" role="doc-backlink"><span class="sectnum">2.3.1 </span>Pairing delimiters</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow></math></p></td>
<td><p><span class="docutils literal">( )</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&lang;</mo><mo stretchy="false">&rang;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\langle \rangle</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">[</mo><mo stretchy="false">]</mo></mrow></math></p></td>
<td><p><span class="docutils literal">[ ]</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&lceil;</mo><mo>&rceil;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\lceil \rceil</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">{</mo><mo stretchy="false">}</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\{ \}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&lfloor;</mo><mo>&rfloor;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\lfloor \rfloor</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\lvert \rvert</span></p></td>
<td><p><span class="docutils literal">\lvert \rvert</span></p></td>
<td><p><span class="math problematic">\lgroup \rgroup</span></p></td>
<td><p><span class="docutils literal">\lgroup \rgroup</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\lVert \rVert</span></p></td>
<td><p><span class="docutils literal">\lVert \rVert</span></p></td>
<td><p><span class="math problematic">\lmoustache \rmoustache</span></p></td>
<td><p><span class="docutils literal">\lmoustache \rmoustache</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 224)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lvert in equation, Line 1.
Unknown command \rvert in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 224)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lgroup in equation, Line 1.
Unknown command \rgroup in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 225)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lVert in equation, Line 1.
Unknown command \rVert in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 225)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lmoustache in equation, Line 1.
Unknown command \rmoustache in equation, Line 1.</p>
</aside>
</section>
<section id="nonpairing-delimiters">
<h4><a class="toc-backref" href="#toc-entry-7" role="doc-backlink"><span class="sectnum">2.3.2 </span>Nonpairing delimiters</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&verbar;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">|</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&verbar;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\vert</span></p></td>
<td><p><span class="math problematic">\arrowvert</span></p></td>
<td><p><span class="docutils literal">\arrowvert</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&Verbar;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\|</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&Verbar;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Vert</span></p></td>
<td><p><span class="math problematic">\Arrowvert</span></p></td>
<td><p><span class="docutils literal">\Arrowvert</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">/</mo></mrow></math></p></td>
<td><p><span class="docutils literal">/</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bsol;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\backslash</span></p></td>
<td><p><span class="math problematic">\bracevert</span></p></td>
<td><p><span class="docutils literal">\bracevert</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 234)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \arrowvert in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 235)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Arrowvert in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 236)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \bracevert in equation, Line 1.</p>
</aside>
<p>The use of <span class="docutils literal">|</span> and <span class="docutils literal">\|</span> for pairs of vertical bars may produce
incorrect spacing, e.g., <span class="docutils literal"><span class="pre">|k|=|-k|</span></span> produces <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&verbar;</mo><mi>k</mi><mo stretchy="false">&verbar;</mo><mo>=</mo><mo stretchy="false">&verbar;</mo><mo>-</mo><mi>k</mi><mo stretchy="false">&verbar;</mo></mrow></math> and
<span class="docutils literal">|\sin(x)|</span> produces <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&verbar;</mo><mi>sin</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">&verbar;</mo></mrow></math>. The pairing delimiters, e.g.
<span class="math problematic">\lvert -k\rvert</span> and <span class="math problematic">\lvert\sin(x)\rvert</span>, prevent this problem.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 239)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lvert in equation, Line 1.
Unknown command \rvert in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 239)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lvert in equation, Line 1.
Unknown command \rvert in equation, Line 1.</p>
</aside>
</section>
</section>
<section id="extensible-vertical-arrows">
<h3><a class="toc-backref" href="#toc-entry-8" role="doc-backlink"><span class="sectnum">2.4 </span>Extensible vertical arrows</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&uarr;</mo></mrow></math>     <span class="docutils literal">\uparrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&uArr;</mo></mrow></math>     <span class="docutils literal">\Uparrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&darr;</mo></mrow></math>   <span class="docutils literal">\downarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&dArr;</mo></mrow></math>   <span class="docutils literal">\Downarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&updownarrow;</mo></mrow></math> <span class="docutils literal">\updownarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&Updownarrow;</mo></mrow></math> <span class="docutils literal">\Updownarrow</span></p></td>
</tr>
</tbody>
</table>
</section>
<section id="functions-named-operators">
<h3><a class="toc-backref" href="#toc-entry-9" role="doc-backlink"><span class="sectnum">2.5 </span>Functions (named operators)</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>arccos</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\arccos</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>gcd</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\gcd</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&Pr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Pr</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>arcsin</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\arcsin</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>hom</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\hom</span></p></td>
<td><p><span class="math problematic">\projlim</span></p></td>
<td><p><span class="docutils literal">\projlim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>arctan</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\arctan</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>inf</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\inf</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>sec</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\sec</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>arg</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\arg</span></p></td>
<td><p><span class="math problematic">\injlim</span></p></td>
<td><p><span class="docutils literal">\injlim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>sin</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\sin</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>cos</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\cos</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>ker</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\ker</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>sinh</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\sinh</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>cosh</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\cosh</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>lg</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\lg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>sup</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sup</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>cot</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\cot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>lim</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\lim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>tan</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\tan</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>coth</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\coth</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>liminf</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\liminf</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>tanh</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\tanh</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>csc</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\csc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>limsup</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\limsup</span></p></td>
<td><p><span class="math problematic">\varlimsup</span></p></td>
<td><p><span class="docutils literal">\varlimsup</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>deg</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\deg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>ln</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\ln</span></p></td>
<td><p><span class="math problematic">\varliminf</span></p></td>
<td><p><span class="docutils literal">\varliminf</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>det</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\det</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>log</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\log</span></p></td>
<td><p><span class="math problematic">\varprojlim</span></p></td>
<td><p><span class="docutils literal">\varprojlim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>dim</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\dim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>max</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\max</span></p></td>
<td><p><span class="math problematic">\varinjlim</span></p></td>
<td><p><span class="docutils literal">\varinjlim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>exp</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\exp</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>min</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\min</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 262)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \projlim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 264)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \injlim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 269)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varlimsup in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 270)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varliminf in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 271)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varprojlim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 272)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varinjlim in equation, Line 1.</p>
</aside>
<p>Named operators outside the above list can be typeset with
<span class="docutils literal">\operatorname{name}</span>, e.g.</p>
<pre class="math problematic">
\operatorname{sgn}(-3) = -1.
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 279)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \operatorname in equation, Line 1.</p>
</aside>
<!-- TODO: \operatorname* for function name with limits. -->
<p>The <span class="docutils literal">\DeclareMathOperator</span> command can only be used in the
<a class="reference external" href="latex.html#latex-preamble">LaTeX preamble</a>.</p>
</section>
<section id="greek-letters">
<h3><a class="toc-backref" href="#toc-entry-10" role="doc-backlink"><span class="sectnum">2.6 </span>Greek letters</a></h3>
<p>Greek letters that have Latin look-alikes are rarely used in math
formulas and not supported by LaTeX.</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Gamma;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Gamma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&alpha;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\alpha</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&mu;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\mu</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&omega;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\omega</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Delta;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Delta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&beta;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\beta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&nu;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\nu</span></p></td>
<td><p><span class="math problematic">\digamma</span></p></td>
<td><p><span class="docutils literal">\digamma</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Lambda;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Lambda</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&gamma;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\gamma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&xi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\xi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&epsiv;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\varepsilon</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Phi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Phi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&delta;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\delta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&pi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\pi</span></p></td>
<td><p><span class="math problematic">\varkappa</span></p></td>
<td><p><span class="docutils literal">\varkappa</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Pi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Pi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&epsi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\epsilon</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&rho;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\rho</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&phiv;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\varphi</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Psi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Psi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&zeta;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\zeta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&sigma;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\sigma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&piv;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\varpi</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Sigma;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Sigma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&eta;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\eta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&tau;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\tau</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&rhov;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\varrho</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Theta;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Theta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&theta;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\theta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&upsi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\upsilon</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&sigmav;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\varsigma</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Upsi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Upsilon</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&iota;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\iota</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&phi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\phi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&thetav;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\vartheta</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Xi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Xi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&kappa;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\kappa</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&chi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\chi</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&Omega;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\Omega</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&lambda;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\lambda</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&psi;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\psi</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 299)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \digamma in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 301)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varkappa in equation, Line 1.</p>
</aside>
<p>In LaTeX, the default font for capital Greek letters is upright/roman.
<em>Italic</em> capital Greek letters can be obtained by loading a <a class="reference external" href="https://mirrors.ctan.org/macros/latex/contrib/isomath/isomath.html#table-2">package
providing the &quot;ISO&quot; math style</a>. They are used by default in MathML.</p>
<p>Individual Greek italic capitals can also be achieved preceding the
letter name with <span class="docutils literal">var</span> like <span class="docutils literal">\varPhi</span>:
<span class="math problematic">\varGamma\ \varDelta\ \varLambda\ \varPhi\ \varPi\ \varPsi\ \varSigma\
\varTheta\ \varUpsilon\ \varXi\ \varOmega</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 315)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varGamma in equation, Line 1.
Unknown command \varDelta in equation, Line 1.
Unknown command \varLambda in equation, Line 1.
Unknown command \varPhi in equation, Line 1.
Unknown command \varPi in equation, Line 1.
Unknown command \varPsi in equation, Line 1.
Unknown command \varSigma in equation, Line 1.
Unknown command \varTheta in equation, Line 2.
Unknown command \varUpsilon in equation, Line 2.
Unknown command \varXi in equation, Line 2.
Unknown command \varOmega in equation, Line 2.</p>
</aside>
</section>
<section id="letterlike-symbols">
<h3><a class="toc-backref" href="#toc-entry-11" role="doc-backlink"><span class="sectnum">2.7 </span>Letterlike symbols</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&forall;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\forall</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&aleph;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\aleph</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>&hbar;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\hbar</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&ell;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\ell</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\complement</span></p></td>
<td><p><span class="docutils literal">\complement</span></p></td>
<td><p><span class="math problematic">\beth</span></p></td>
<td><p><span class="docutils literal">\beth</span></p></td>
<td><p><span class="math problematic">\hslash</span></p></td>
<td><p><span class="docutils literal">\hslash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&weierp;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\wp</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&exist;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\exists</span></p></td>
<td><p><span class="math problematic">\gimel</span></p></td>
<td><p><span class="docutils literal">\gimel</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&Im;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Im</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&real;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Re</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\Finv</span></p></td>
<td><p><span class="docutils literal">\Finv</span></p></td>
<td><p><span class="math problematic">\daleth</span></p></td>
<td><p><span class="docutils literal">\daleth</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&imath;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\imath</span></p></td>
<td><p><span class="math problematic">\circledR</span></p></td>
<td><p><span class="docutils literal">\circledR</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\Game</span></p></td>
<td><p><span class="docutils literal">\Game</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&part;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\partial</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&jmath;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\jmath</span></p></td>
<td><p><span class="math problematic">\circledS</span></p></td>
<td><p><span class="docutils literal">\circledS</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&mho;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\mho</span></p></td>
<td><p><span class="math problematic">\eth</span></p></td>
<td><p><span class="docutils literal">\eth</span></p></td>
<td><p><span class="math problematic">\Bbbk</span></p></td>
<td><p><span class="docutils literal">\Bbbk</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 330)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \complement in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 330)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \beth in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 330)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \hslash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 331)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gimel in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 332)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Finv in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 332)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \daleth in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 332)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circledR in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 333)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Game in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 333)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circledS in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 334)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \eth in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 334)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Bbbk in equation, Line 1.</p>
</aside>
</section>
<section id="math-alphabets">
<span id="math-alphabet"></span><h3><a class="toc-backref" href="#toc-entry-12" role="doc-backlink"><span class="sectnum">2.8 </span>Math alphabets</a></h3>
<p>The TeX <em>math alphabet</em> macros are intended for mathematical variables
where style variations are important semantically.
They style letters and numbers with a combination of font attributes
(shape, weight, family) --- non-alphanumerical symbols, function names,
and mathematical text are left unchanged.</p>
<p>MathML uses the <em>mathvariant</em> <a class="reference external" href="https://www.w3.org/TR/mathml4/#presm_commatt">style attribute</a> or pre-styled characters
from the <a class="reference external" href="https://en.wikipedia.org/wiki/Mathematical_Alphanumeric_Symbols">Mathematical Alphanumeric Symbols</a> Unicode block.</p>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\mathrm</span></p></td>
<td><p><span class="docutils literal">s_\mathrm{out}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<msub><mrow><mi>s</mi></mrow><mrow><mi fontstyle="normal">out</mi></mrow>
</msub>
</mrow></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathbf</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\mathbf{r}^2=x^2+y^2</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<msup><mrow><mi mathvariant="bold">r</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>=</mo>
<msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>+</mo>
<msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
</mrow></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathit</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\mathit{\sin\Gamma}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi fontstyle="italic">sin</mi><mi fontstyle="italic">&Gamma;</mi></mrow></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathcal</span></p></td>
<td><p><span class="docutils literal">\mathcal{F}f(x)</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi fontstyle="italic">F</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathbb</span></p></td>
<td><p><span class="docutils literal">\mathbb{R \subset C}</span></p></td>
<td><p><span class="math problematic">\mathbb{R \subset C}</span></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathfrak</span></p></td>
<td><p><span class="docutils literal">\mathfrak{a+b}</span></p></td>
<td><p><span class="math problematic">\mathfrak{a+b}</span></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathsf</span></p></td>
<td><p><span class="docutils literal">\mathsf x</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mstyle fontfamily="helvetica"><mi>x</mi></mstyle></mrow>
</mrow></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathtt</span></p></td>
<td><p><span class="docutils literal">\mathtt{0.12}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>0</mn><mo fontfamily="courier" fontstyle="normal">.</mo><mn>12</mn></mrow></math></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 361)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbb in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 362)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathfrak in equation, Line 1.</p>
</aside>
<p>The set of characters in a given &quot;math alphabet&quot; varies.
LaTeX may produce garbage for unsupported characters.
Additional math alphabets are defined in LaTeX packages, e.g.,</p>
<ul class="simple">
<li><p><span class="docutils literal">\mathbfit</span> from <a class="reference external" href="https://www.ctan.org/pkg/isomath">isomath</a> allows vector symbols in line with the
International Standard <a class="citation-reference" href="#iso-80000-2" id="citation-reference-1" role="doc-biblioref">[ISO-80000-2]</a>.
E.g., <span class="docutils literal"><span class="pre">\mathbfit{r}^2=x^2+y^2</span></span> becomes <span class="math problematic">\mathbfit{r}^2=x^2+y^2</span>.</p></li>
<li><p>Several packages, e.g. <a class="reference external" href="https://www.ctan.org/pkg/mathrsfs">mathrsfs</a>, define <span class="docutils literal">\mathscr</span> that selects a
differently shaped &quot;script&quot; alphabet.</p></li>
</ul>
<p>The listing below shows the characters supported by Unicode and
Docutils with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> MathML. <a class="brackets" href="#italic-digits" id="footnote-reference-3" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 371)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbfit in equation, Line 1.</p>
</aside>
<dl class="simple">
<dt>default:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi><mi>&ensp;</mi><mi mathvariant="italic">abcdefghijklmnopqrstuvwxyz</mi><mi>&ensp;</mi><mi mathvariant="italic">&imath;</mi><mi mathvariant="italic">&jmath;</mi></mrow></math>
<span class="math problematic">{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇}</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>0123456789</mn></mrow></math></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 382)</p>
<p>'latin-1' codec can't encode character '\u03dc' in position 280: ordinal not in range(256)</p>
</aside>
</dd>
<dt>mathrm:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi fontstyle="normal">ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi><mi fontstyle="normal">&ensp;</mi><mi fontstyle="normal">abcdefghijklmnopqrstuvwxyz</mi><mi fontstyle="normal">&ensp;</mi><mi fontstyle="normal">&imath;</mi><mi fontstyle="normal">&jmath;</mi></mrow></math>
<span class="math problematic">\mathrm{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇}</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>0123456789</mn></mrow></math></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 386)</p>
<p>'latin-1' codec can't encode character '\u03dc' in position 287: ordinal not in range(256)</p>
</aside>
</dd>
<dt>mathbf:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="bold">ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi><mi mathvariant="bold">&ensp;</mi><mi mathvariant="bold">abcdefghijklmnopqrstuvwxyz</mi></mrow></math>
<span class="math problematic">\mathbf{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇}</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>0123456789</mn></mrow></math></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 390)</p>
<p>'latin-1' codec can't encode character '\u03dc' in position 287: ordinal not in range(256)</p>
</aside>
</dd>
<dt>mathit:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi fontstyle="italic">ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi><mi fontstyle="italic">&ensp;</mi><mi fontstyle="italic">abcdefghijklmnopqrstuvwxyz</mi><mi fontstyle="italic">&ensp;</mi><mi fontstyle="italic">&imath;</mi><mi fontstyle="italic">&jmath;</mi></mrow></math>
<span class="math problematic">\mathit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>0123456789</mn></mrow></math> <a class="brackets" href="#italic-digits" id="footnote-reference-4" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 394)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varkappa in equation, Line 1.</p>
</aside>
</dd>
<dt>mathbfit:</dt>
<dd><p><span class="math problematic">\mathbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span>
<span class="math problematic">\mathbfit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 398)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbfit in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 398)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbfit in equation, Line 1.
Unknown command \varkappa in equation, Line 1.</p>
</aside>
</dd>
<dt>mathcal:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi fontstyle="italic">ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi><mi fontstyle="italic">&ensp;</mi><mi fontstyle="italic">abcdefghijklmnopqrstuvwxyz</mi></mrow></math></p>
</dd>
<dt>mathscr:</dt>
<dd><p><span class="math problematic">\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 403)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathscr in equation, Line 1.</p>
</aside>
</dd>
<dt>mathbb:</dt>
<dd><p><span class="math problematic">\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span>
<span class="math problematic">\mathbb{ΓΠΣ\ γπ}</span>
<span class="math problematic">\mathbb{0123456789}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 405)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbb in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 405)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbb in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 405)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbb in equation, Line 1.</p>
</aside>
</dd>
<dt>mathfrak:</dt>
<dd><p><span class="math problematic">\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 409)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathfrak in equation, Line 1.</p>
</aside>
</dd>
<dt>mathsf:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mstyle fontfamily="helvetica"><mi mathvariant="italic">ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi><mi>&ensp;</mi><mi mathvariant="italic">abcdefghijklmnopqrstuvwxyz</mi></mstyle></mrow>
</mrow></math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mstyle fontfamily="helvetica"><mn>0123456789</mn></mstyle></mrow>
</mrow></math></p>
</dd>
<dt>mathsfit:</dt>
<dd><p><span class="math problematic">\mathsfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 414)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathsfit in equation, Line 1.</p>
</aside>
</dd>
<dt>mathsfbfit:</dt>
<dd><p><span class="math problematic">\mathsfbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span>
<span class="math problematic">\mathsfbfit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 416)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathsfbfit in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 416)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathsfbfit in equation, Line 1.
Unknown command \varkappa in equation, Line 1.</p>
</aside>
</dd>
<dt>mathtt:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi fontfamily="courier" fontstyle="normal">ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi><mi fontfamily="courier" fontstyle="normal">&ensp;</mi><mi fontfamily="courier" fontstyle="normal">abcdefghijklmnopqrstuvwxyz</mi></mrow></math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>0123456789</mn></mrow></math></p>
</dd>
</dl>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="italic-digits" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#footnote-reference-3">1</a>,<a role="doc-backlink" href="#footnote-reference-4">2</a>)</span>
<p>Italic digits are not defined in Unicode
but work in LaTeX.</p>
</aside>
</aside>
<p>In contrast to the <em>math alphabet</em> selectors, <span class="docutils literal">\boldsymbol</span> only
changes the <em>font weight</em>. It can be used to get a bold version of
any mathematical symbol:</p>
<pre class="math problematic">
V_i x \pm \cos(\alpha) \approx 3\Gamma \quad \forall x\in\mathbb{R}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 429)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbb in equation, Line 1.</p>
</aside>
<pre class="math problematic">
\boldsymbol{V_i x \pm \cos(\alpha) \approx 3\Gamma \quad \forall x\in\mathbb{R}}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 429)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mathbb in equation, Line 1.</p>
</aside>
<p>It is usually ill-advised to apply <span class="docutils literal">\boldsymbol</span> to more than one symbol
at a time.</p>
</section>
<section id="miscellaneous-symbols">
<h3><a class="toc-backref" href="#toc-entry-13" role="doc-backlink"><span class="sectnum">2.9 </span>Miscellaneous symbols</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>#</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\#</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&clubs;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\clubsuit</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&not;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\neg</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>&amp;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\&amp;</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&diams;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\diamondsuit</span></p></td>
<td><p><span class="math problematic">\nexists</span></p></td>
<td><p><span class="docutils literal">\nexists</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&angle;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\angle</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&empty;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\emptyset</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>'</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\prime</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\backprime</span></p></td>
<td><p><span class="docutils literal">\backprime</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&exist;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\exists</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sharp;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sharp</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\bigstar</span></p></td>
<td><p><span class="docutils literal">\bigstar</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&flat;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\flat</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&spades;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\spadesuit</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\blacklozenge</span></p></td>
<td><p><span class="docutils literal">\blacklozenge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&forall;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\forall</span></p></td>
<td><p><span class="math problematic">\sphericalangle</span></p></td>
<td><p><span class="docutils literal">\sphericalangle</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\blacksquare</span></p></td>
<td><p><span class="docutils literal">\blacksquare</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&hearts;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\heartsuit</span></p></td>
<td><p><span class="math problematic">\square</span></p></td>
<td><p><span class="docutils literal">\square</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\blacktriangle</span></p></td>
<td><p><span class="docutils literal">\blacktriangle</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi mathvariant="italic">&infin;</mi></mrow></math></p></td>
<td><p><span class="docutils literal">\infty</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&radic;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\surd</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\blacktriangledown</span></p></td>
<td><p><span class="docutils literal">\blacktriangledown</span></p></td>
<td><p><span class="math problematic">\lozenge</span></p></td>
<td><p><span class="docutils literal">\lozenge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&top;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\top</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bot;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\bot</span></p></td>
<td><p><span class="math problematic">\measuredangle</span></p></td>
<td><p><span class="docutils literal">\measuredangle</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&triangle;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\triangle</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\diagdown</span></p></td>
<td><p><span class="docutils literal">\diagdown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&nabla;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\nabla</span></p></td>
<td><p><span class="math problematic">\triangledown</span></p></td>
<td><p><span class="docutils literal">\triangledown</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\diagup</span></p></td>
<td><p><span class="docutils literal">\diagup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&natural;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\natural</span></p></td>
<td><p><span class="math problematic">\varnothing</span></p></td>
<td><p><span class="docutils literal">\varnothing</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 452)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nexists in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 454)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \backprime in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 455)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \bigstar in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 456)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \blacklozenge in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 456)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \sphericalangle in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 457)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \blacksquare in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 457)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \square in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 458)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \blacktriangle in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 459)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \blacktriangledown in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 459)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lozenge in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 460)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \measuredangle in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 461)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \diagdown in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 461)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \triangledown in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 462)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \diagup in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 462)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varnothing in equation, Line 1.</p>
</aside>
</section>
<section id="punctuation">
<h3><a class="toc-backref" href="#toc-entry-14" role="doc-backlink"><span class="sectnum">2.10 </span>Punctuation</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>.</mo></mrow></math></p></td>
<td><p><span class="docutils literal">.</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>!</mo></mrow></math></p></td>
<td><p><span class="docutils literal">!</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>:</mrow></math></p></td>
<td><p><span class="docutils literal">\vdots</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">/</mo></mrow></math></p></td>
<td><p><span class="docutils literal">/</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>?</mo></mrow></math></p></td>
<td><p><span class="docutils literal">?</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&#x2026;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\dotsb</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&verbar;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">|</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>:</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\colon</span> <a class="brackets" href="#footnote-1" id="footnote-reference-5" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&#x2026;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\dotsc</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>'</mo></mrow></math></p></td>
<td><p><span class="docutils literal">'</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&#x2026;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\cdots</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&#x2026;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\dotsi</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">;</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&dtdot;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\ddots</span></p></td>
<td><p><span class="math problematic">\dotsm</span></p></td>
<td><p><span class="docutils literal">\dotsm</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>:</mo></mrow></math></p></td>
<td><p><span class="docutils literal">:</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&#x2026;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\ldots</span></p></td>
<td><p><span class="math problematic">\dotso</span></p></td>
<td><p><span class="docutils literal">\dotso</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 475)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \dotsm in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 476)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \dotso in equation, Line 1.</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-1" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-5">3</a><span class="fn-bracket">]</span></span>
<p>Punctuation (not ratio):
Compare spacing in <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi><mo>:</mo><mi>b</mi><mo>&rarr;</mo><mi>c</mi></mrow></math> to <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>c</mi></mrow></math>.</p>
</aside>
</aside>
</section>
<section id="relation-symbols">
<h3><a class="toc-backref" href="#toc-entry-15" role="doc-backlink"><span class="sectnum">2.11 </span>Relation symbols</a></h3>
<section id="arrows">
<h4><a class="toc-backref" href="#toc-entry-16" role="doc-backlink"><span class="sectnum">2.11.1 </span>Arrows</a></h4>
<table>
<tbody>
<tr><td><p><span class="math problematic">\circlearrowleft</span></p></td>
<td><p><span class="docutils literal">\circlearrowleft</span></p></td>
<td><p><span class="math problematic">\circlearrowright</span></p></td>
<td><p><span class="docutils literal">\circlearrowright</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\curvearrowleft</span></p></td>
<td><p><span class="docutils literal">\curvearrowleft</span></p></td>
<td><p><span class="math problematic">\curvearrowright</span></p></td>
<td><p><span class="docutils literal">\curvearrowright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&hookleftarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\hookleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&hookrightarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\hookrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&larr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\leftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rarr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\rightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&lArr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Leftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rArr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Rightarrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\leftarrowtail</span></p></td>
<td><p><span class="docutils literal">\leftarrowtail</span></p></td>
<td><p><span class="math problematic">\rightarrowtail</span></p></td>
<td><p><span class="docutils literal">\rightarrowtail</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&leftharpoondown;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\leftharpoondown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rightharpoondown;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\rightharpoondown</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&leftharpoonup;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\leftharpoonup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rightharpoonup;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\rightharpoonup</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\leftleftarrows</span></p></td>
<td><p><span class="docutils literal">\leftleftarrows</span></p></td>
<td><p><span class="math problematic">\rightrightarrows</span></p></td>
<td><p><span class="docutils literal">\rightrightarrows</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&leftrightarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\leftrightarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&Leftrightarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Leftrightarrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\leftrightarrows</span></p></td>
<td><p><span class="docutils literal">\leftrightarrows</span></p></td>
<td><p><span class="math problematic">\rightleftarrows</span></p></td>
<td><p><span class="docutils literal">\rightleftarrows</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\leftrightharpoons</span></p></td>
<td><p><span class="docutils literal">\leftrightharpoons</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rightleftharpoons;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\rightleftharpoons</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\leftrightsquigarrow</span></p></td>
<td><p><span class="docutils literal">\leftrightsquigarrow</span></p></td>
<td><p><span class="math problematic">\rightsquigarrow</span></p></td>
<td><p><span class="docutils literal">\rightsquigarrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\Lleftarrow</span></p></td>
<td><p><span class="docutils literal">\Lleftarrow</span></p></td>
<td><p><span class="math problematic">\Rrightarrow</span></p></td>
<td><p><span class="docutils literal">\Rrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&larr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\longleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rarr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\longrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&lArr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Longleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rArr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Longrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&leftrightarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\longleftrightarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&Longleftrightarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\Longleftrightarrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\looparrowleft</span></p></td>
<td><p><span class="docutils literal">\looparrowleft</span></p></td>
<td><p><span class="math problematic">\looparrowright</span></p></td>
<td><p><span class="docutils literal">\looparrowright</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\Lsh</span></p></td>
<td><p><span class="docutils literal">\Lsh</span></p></td>
<td><p><span class="math problematic">\Rsh</span></p></td>
<td><p><span class="docutils literal">\Rsh</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rarr;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\mapsto</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&longmapsto;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\longmapsto</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\multimap</span></p></td>
<td><p><span class="docutils literal">\multimap</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><span class="math problematic">\nleftarrow</span></p></td>
<td><p><span class="docutils literal">\nleftarrow</span></p></td>
<td><p><span class="math problematic">\nrightarrow</span></p></td>
<td><p><span class="docutils literal">\nrightarrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nLeftarrow</span></p></td>
<td><p><span class="docutils literal">\nLeftarrow</span></p></td>
<td><p><span class="math problematic">\nRightarrow</span></p></td>
<td><p><span class="docutils literal">\nRightarrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nleftrightarrow</span></p></td>
<td><p><span class="docutils literal">\nleftrightarrow</span></p></td>
<td><p><span class="math problematic">\nLeftrightarrow</span></p></td>
<td><p><span class="docutils literal">\nLeftrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&nwarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\nwarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&nearrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\nearrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&swarrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\swarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&searrow;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\searrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\twoheadleftarrow</span></p></td>
<td><p><span class="docutils literal">\twoheadleftarrow</span></p></td>
<td><p><span class="math problematic">\twoheadrightarrow</span></p></td>
<td><p><span class="docutils literal">\twoheadrightarrow</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\upharpoonleft</span></p></td>
<td><p><span class="docutils literal">\upharpoonleft</span></p></td>
<td><p><span class="math problematic">\upharpoonright</span></p></td>
<td><p><span class="docutils literal">\upharpoonright</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\downharpoonleft</span></p></td>
<td><p><span class="docutils literal">\downharpoonleft</span></p></td>
<td><p><span class="math problematic">\downharpoonright</span></p></td>
<td><p><span class="docutils literal">\downharpoonright</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\upuparrows</span></p></td>
<td><p><span class="docutils literal">\upuparrows</span></p></td>
<td><p><span class="math problematic">\downdownarrows</span></p></td>
<td><p><span class="docutils literal">\downdownarrows</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 491)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circlearrowleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 491)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circlearrowright in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 492)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \curvearrowleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 492)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \curvearrowright in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 496)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leftarrowtail in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 496)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \rightarrowtail in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 499)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leftleftarrows in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 499)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \rightrightarrows in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 501)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leftrightarrows in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 501)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \rightleftarrows in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 502)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leftrightharpoons in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 503)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leftrightsquigarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 503)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \rightsquigarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 504)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Lleftarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 504)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Rrightarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 508)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \looparrowleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 508)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \looparrowright in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 509)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Lsh in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 509)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Rsh in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 511)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \multimap in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 512)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nleftarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 512)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nrightarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 513)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nLeftarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 513)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nRightarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 514)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nleftrightarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 514)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nLeftrightarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 517)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \twoheadleftarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 517)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \twoheadrightarrow in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 518)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \upharpoonleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 518)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \upharpoonright in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 519)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \downharpoonleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 519)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \downharpoonright in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 520)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \upuparrows in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 520)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \downdownarrows in equation, Line 1.</p>
</aside>
<p>Synonyms: <span class="math problematic">\gets</span> <span class="docutils literal">\gets</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&rarr;</mo></mrow></math> <span class="docutils literal">\to</span>, <span class="math problematic">\restriction</span> <span class="docutils literal">\restriction</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 523)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gets in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 523)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \restriction in equation, Line 1.</p>
</aside>
</section>
<section id="comparison">
<h4><a class="toc-backref" href="#toc-entry-17" role="doc-backlink"><span class="sectnum">2.11.2 </span>Comparison</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&lt;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">&lt;</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ge;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\geq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo> &lt;&lt; </mo></mrow></math></p></td>
<td><p><span class="docutils literal">\ll</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&prec;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\prec</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>=</mo></mrow></math></p></td>
<td><p><span class="docutils literal">=</span></p></td>
<td><p><span class="math problematic">\geqq</span></p></td>
<td><p><span class="docutils literal">\geqq</span></p></td>
<td><p><span class="math problematic">\lll</span></p></td>
<td><p><span class="docutils literal">\lll</span></p></td>
<td><p><span class="math problematic">\precapprox</span></p></td>
<td><p><span class="docutils literal">\precapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&gt;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">&gt;</span></p></td>
<td><p><span class="math problematic">\geqslant</span></p></td>
<td><p><span class="docutils literal">\geqslant</span></p></td>
<td><p><span class="math problematic">\lnapprox</span></p></td>
<td><p><span class="docutils literal">\lnapprox</span></p></td>
<td><p><span class="math problematic">\preccurlyeq</span></p></td>
<td><p><span class="docutils literal">\preccurlyeq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ap;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\approx</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&gt;&gt;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\gg</span></p></td>
<td><p><span class="math problematic">\lneq</span></p></td>
<td><p><span class="docutils literal">\lneq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&preceq;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\preceq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\approxeq</span></p></td>
<td><p><span class="docutils literal">\approxeq</span></p></td>
<td><p><span class="math problematic">\ggg</span></p></td>
<td><p><span class="docutils literal">\ggg</span></p></td>
<td><p><span class="math problematic">\lneqq</span></p></td>
<td><p><span class="docutils literal">\lneqq</span></p></td>
<td><p><span class="math problematic">\precnapprox</span></p></td>
<td><p><span class="docutils literal">\precnapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&asymp;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\asymp</span></p></td>
<td><p><span class="math problematic">\gnapprox</span></p></td>
<td><p><span class="docutils literal">\gnapprox</span></p></td>
<td><p><span class="math problematic">\lnsim</span></p></td>
<td><p><span class="docutils literal">\lnsim</span></p></td>
<td><p><span class="math problematic">\precneqq</span></p></td>
<td><p><span class="docutils literal">\precneqq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\backsim</span></p></td>
<td><p><span class="docutils literal">\backsim</span></p></td>
<td><p><span class="math problematic">\gneq</span></p></td>
<td><p><span class="docutils literal">\gneq</span></p></td>
<td><p><span class="math problematic">\ncong</span></p></td>
<td><p><span class="docutils literal">\ncong</span></p></td>
<td><p><span class="math problematic">\precnsim</span></p></td>
<td><p><span class="docutils literal">\precnsim</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\backsimeq</span></p></td>
<td><p><span class="docutils literal">\backsimeq</span></p></td>
<td><p><span class="math problematic">\gneqq</span></p></td>
<td><p><span class="docutils literal">\gneqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ne;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\neq</span></p></td>
<td><p><span class="math problematic">\precsim</span></p></td>
<td><p><span class="docutils literal">\precsim</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\bumpeq</span></p></td>
<td><p><span class="docutils literal">\bumpeq</span></p></td>
<td><p><span class="math problematic">\gnsim</span></p></td>
<td><p><span class="docutils literal">\gnsim</span></p></td>
<td><p><span class="math problematic">\ngeq</span></p></td>
<td><p><span class="docutils literal">\ngeq</span></p></td>
<td><p><span class="math problematic">\risingdotseq</span></p></td>
<td><p><span class="docutils literal">\risingdotseq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\Bumpeq</span></p></td>
<td><p><span class="docutils literal">\Bumpeq</span></p></td>
<td><p><span class="math problematic">\gtrapprox</span></p></td>
<td><p><span class="docutils literal">\gtrapprox</span></p></td>
<td><p><span class="math problematic">\ngeqq</span></p></td>
<td><p><span class="docutils literal">\ngeqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>~</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sim</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\circeq</span></p></td>
<td><p><span class="docutils literal">\circeq</span></p></td>
<td><p><span class="math problematic">\gtreqless</span></p></td>
<td><p><span class="docutils literal">\gtreqless</span></p></td>
<td><p><span class="math problematic">\ngeqslant</span></p></td>
<td><p><span class="docutils literal">\ngeqslant</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ap;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\simeq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&cong;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\cong</span></p></td>
<td><p><span class="math problematic">\gtreqqless</span></p></td>
<td><p><span class="docutils literal">\gtreqqless</span></p></td>
<td><p><span class="math problematic">\ngtr</span></p></td>
<td><p><span class="docutils literal">\ngtr</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&succ;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\succ</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\curlyeqprec</span></p></td>
<td><p><span class="docutils literal">\curlyeqprec</span></p></td>
<td><p><span class="math problematic">\gtrless</span></p></td>
<td><p><span class="docutils literal">\gtrless</span></p></td>
<td><p><span class="math problematic">\nleq</span></p></td>
<td><p><span class="docutils literal">\nleq</span></p></td>
<td><p><span class="math problematic">\succapprox</span></p></td>
<td><p><span class="docutils literal">\succapprox</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\curlyeqsucc</span></p></td>
<td><p><span class="docutils literal">\curlyeqsucc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&gt;~</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\gtrsim</span></p></td>
<td><p><span class="math problematic">\nleqq</span></p></td>
<td><p><span class="docutils literal">\nleqq</span></p></td>
<td><p><span class="math problematic">\succcurlyeq</span></p></td>
<td><p><span class="docutils literal">\succcurlyeq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&doteq;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\doteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&le;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\leq</span></p></td>
<td><p><span class="math problematic">\nleqslant</span></p></td>
<td><p><span class="docutils literal">\nleqslant</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&succeq;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\succeq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\doteqdot</span></p></td>
<td><p><span class="docutils literal">\doteqdot</span></p></td>
<td><p><span class="math problematic">\leqq</span></p></td>
<td><p><span class="docutils literal">\leqq</span></p></td>
<td><p><span class="math problematic">\nless</span></p></td>
<td><p><span class="docutils literal">\nless</span></p></td>
<td><p><span class="math problematic">\succnapprox</span></p></td>
<td><p><span class="docutils literal">\succnapprox</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\eqcirc</span></p></td>
<td><p><span class="docutils literal">\eqcirc</span></p></td>
<td><p><span class="math problematic">\leqslant</span></p></td>
<td><p><span class="docutils literal">\leqslant</span></p></td>
<td><p><span class="math problematic">\nprec</span></p></td>
<td><p><span class="docutils literal">\nprec</span></p></td>
<td><p><span class="math problematic">\succneqq</span></p></td>
<td><p><span class="docutils literal">\succneqq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\eqsim</span></p></td>
<td><p><span class="docutils literal">\eqsim</span></p></td>
<td><p><span class="math problematic">\lessapprox</span></p></td>
<td><p><span class="docutils literal">\lessapprox</span></p></td>
<td><p><span class="math problematic">\npreceq</span></p></td>
<td><p><span class="docutils literal">\npreceq</span></p></td>
<td><p><span class="math problematic">\succnsim</span></p></td>
<td><p><span class="docutils literal">\succnsim</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\eqslantgtr</span></p></td>
<td><p><span class="docutils literal">\eqslantgtr</span></p></td>
<td><p><span class="math problematic">\lesseqgtr</span></p></td>
<td><p><span class="docutils literal">\lesseqgtr</span></p></td>
<td><p><span class="math problematic">\nsim</span></p></td>
<td><p><span class="docutils literal">\nsim</span></p></td>
<td><p><span class="math problematic">\succsim</span></p></td>
<td><p><span class="docutils literal">\succsim</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\eqslantless</span></p></td>
<td><p><span class="docutils literal">\eqslantless</span></p></td>
<td><p><span class="math problematic">\lesseqqgtr</span></p></td>
<td><p><span class="docutils literal">\lesseqqgtr</span></p></td>
<td><p><span class="math problematic">\nsucc</span></p></td>
<td><p><span class="docutils literal">\nsucc</span></p></td>
<td><p><span class="math problematic">\thickapprox</span></p></td>
<td><p><span class="docutils literal">\thickapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&equiv;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\equiv</span></p></td>
<td><p><span class="math problematic">\lessgtr</span></p></td>
<td><p><span class="docutils literal">\lessgtr</span></p></td>
<td><p><span class="math problematic">\nsucceq</span></p></td>
<td><p><span class="docutils literal">\nsucceq</span></p></td>
<td><p><span class="math problematic">\thicksim</span></p></td>
<td><p><span class="docutils literal">\thicksim</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\fallingdotseq</span></p></td>
<td><p><span class="docutils literal">\fallingdotseq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&lt;~</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\lesssim</span></p></td>
<td></td>
<td></td>
<td><p><span class="math problematic">\triangleq</span></p></td>
<td><p><span class="docutils literal">\triangleq</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 532)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \geqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 532)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lll in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 532)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \precapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 533)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \geqslant in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 533)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lnapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 533)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \preccurlyeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 534)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lneq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 535)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \approxeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 535)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ggg in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 535)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lneqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 535)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \precnapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 536)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gnapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 536)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lnsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 536)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \precneqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 537)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \backsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 537)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gneq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 537)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ncong in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 537)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \precnsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 538)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \backsimeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 538)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gneqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 538)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \precsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 539)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \bumpeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 539)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gnsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 539)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ngeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 539)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \risingdotseq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 540)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Bumpeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 540)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gtrapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 540)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ngeqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 541)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \circeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 541)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gtreqless in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 541)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ngeqslant in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 542)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gtreqqless in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 542)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ngtr in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 543)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \curlyeqprec in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 543)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gtrless in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 543)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nleq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 543)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \succapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 544)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \curlyeqsucc in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 544)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nleqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 544)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \succcurlyeq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 545)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nleqslant in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 546)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \doteqdot in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 546)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 546)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nless in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 546)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \succnapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 547)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \eqcirc in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 547)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \leqslant in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 547)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nprec in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 547)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \succneqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 548)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \eqsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 548)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lessapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 548)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \npreceq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 548)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \succnsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 549)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \eqslantgtr in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 549)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lesseqgtr in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 549)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 549)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \succsim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 550)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \eqslantless in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 550)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lesseqqgtr in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 550)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nsucc in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 550)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \thickapprox in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 551)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lessgtr in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 551)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nsucceq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 551)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \thicksim in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 552)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \fallingdotseq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 552)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \triangleq in equation, Line 1.</p>
</aside>
<p>The commands <span class="docutils literal">\lvertneqq</span> and <span class="docutils literal">\gvertneqq</span> are not supported
with MathML output, as there is no corresponding Unicode character.</p>
<p>Synonyms: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ne;</mo></mrow></math> <span class="docutils literal">\ne</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&le;</mo></mrow></math> <span class="docutils literal">\le</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ge;</mo></mrow></math> <span class="docutils literal">\ge</span>,
<span class="math problematic">\Doteq</span> <span class="docutils literal">\Doteq</span>, <span class="math problematic">\llless</span> <span class="docutils literal">\llless</span>, <span class="math problematic">\gggtr</span> <span class="docutils literal">\gggtr</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 558)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Doteq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 558)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \llless in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 558)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \gggtr in equation, Line 1.</p>
</aside>
<p>Symbols can be negated prepending <span class="docutils literal">\not</span>, e.g.
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ne;</mo></mrow></math> <span class="docutils literal">\not=</span>, <span class="math problematic">\not\equiv</span> <span class="docutils literal">\not\equiv</span>,
<span class="math problematic">\not\gtrless</span> <span class="docutils literal">\not\gtrless</span>, <span class="math problematic">\not\lessgtr</span> <span class="docutils literal">\not\lessgtr</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 561)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \not in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 561)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \not in equation, Line 1.
Unknown command \gtrless in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 561)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \not in equation, Line 1.
Unknown command \lessgtr in equation, Line 1.</p>
</aside>
</section>
<section id="miscellaneous-relations">
<h4><a class="toc-backref" href="#toc-entry-18" role="doc-backlink"><span class="sectnum">2.11.3 </span>Miscellaneous relations</a></h4>
<table>
<tbody>
<tr><td><p><span class="math problematic">\backepsilon</span></p></td>
<td><p><span class="docutils literal">\backepsilon</span></p></td>
<td><p><span class="math problematic">\ntrianglelefteq</span></p></td>
<td><p><span class="docutils literal">\ntrianglelefteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sube;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\subseteq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\because</span></p></td>
<td><p><span class="docutils literal">\because</span></p></td>
<td><p><span class="math problematic">\ntriangleright</span></p></td>
<td><p><span class="docutils literal">\ntriangleright</span></p></td>
<td><p><span class="math problematic">\subseteqq</span></p></td>
<td><p><span class="docutils literal">\subseteqq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\between</span></p></td>
<td><p><span class="docutils literal">\between</span></p></td>
<td><p><span class="math problematic">\ntrianglerighteq</span></p></td>
<td><p><span class="docutils literal">\ntrianglerighteq</span></p></td>
<td><p><span class="math problematic">\subsetneq</span></p></td>
<td><p><span class="docutils literal">\subsetneq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\blacktriangleleft</span></p></td>
<td><p><span class="docutils literal">\blacktriangleleft</span></p></td>
<td><p><span class="math problematic">\nvdash</span></p></td>
<td><p><span class="docutils literal">\nvdash</span></p></td>
<td><p><span class="math problematic">\subsetneqq</span></p></td>
<td><p><span class="docutils literal">\subsetneqq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\blacktriangleright</span></p></td>
<td><p><span class="docutils literal">\blacktriangleright</span></p></td>
<td><p><span class="math problematic">\nVdash</span></p></td>
<td><p><span class="docutils literal">\nVdash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sup;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\supset</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bowtie;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\bowtie</span></p></td>
<td><p><span class="math problematic">\nvDash</span></p></td>
<td><p><span class="docutils literal">\nvDash</span></p></td>
<td><p><span class="math problematic">\Supset</span></p></td>
<td><p><span class="docutils literal">\Supset</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&dashv;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\dashv</span></p></td>
<td><p><span class="math problematic">\nVDash</span></p></td>
<td><p><span class="docutils literal">\nVDash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&supe;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\supseteq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&frown;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\frown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&parallel;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\parallel</span></p></td>
<td><p><span class="math problematic">\supseteqq</span></p></td>
<td><p><span class="docutils literal">\supseteqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&isin;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\in</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bottom;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\perp</span></p></td>
<td><p><span class="math problematic">\supsetneq</span></p></td>
<td><p><span class="docutils literal">\supsetneq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&mid;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\mid</span></p></td>
<td><p><span class="math problematic">\pitchfork</span></p></td>
<td><p><span class="docutils literal">\pitchfork</span></p></td>
<td><p><span class="math problematic">\supsetneqq</span></p></td>
<td><p><span class="docutils literal">\supsetneqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&models;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\models</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&prop;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\propto</span></p></td>
<td><p><span class="math problematic">\therefore</span></p></td>
<td><p><span class="docutils literal">\therefore</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&ni;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\ni</span></p></td>
<td><p><span class="math problematic">\shortmid</span></p></td>
<td><p><span class="docutils literal">\shortmid</span></p></td>
<td><p><span class="math problematic">\trianglelefteq</span></p></td>
<td><p><span class="docutils literal">\trianglelefteq</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nmid</span></p></td>
<td><p><span class="docutils literal">\nmid</span></p></td>
<td><p><span class="math problematic">\shortparallel</span></p></td>
<td><p><span class="docutils literal">\shortparallel</span></p></td>
<td><p><span class="math problematic">\trianglerighteq</span></p></td>
<td><p><span class="docutils literal">\trianglerighteq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&notin;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\notin</span></p></td>
<td><p><span class="math problematic">\smallfrown</span></p></td>
<td><p><span class="docutils literal">\smallfrown</span></p></td>
<td><p><span class="math problematic">\varpropto</span></p></td>
<td><p><span class="docutils literal">\varpropto</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nparallel</span></p></td>
<td><p><span class="docutils literal">\nparallel</span></p></td>
<td><p><span class="math problematic">\smallsmile</span></p></td>
<td><p><span class="docutils literal">\smallsmile</span></p></td>
<td><p><span class="math problematic">\vartriangle</span></p></td>
<td><p><span class="docutils literal">\vartriangle</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nshortmid</span></p></td>
<td><p><span class="docutils literal">\nshortmid</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&smile;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\smile</span></p></td>
<td><p><span class="math problematic">\vartriangleleft</span></p></td>
<td><p><span class="docutils literal">\vartriangleleft</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nshortparallel</span></p></td>
<td><p><span class="docutils literal">\nshortparallel</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sqsubset;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sqsubset</span></p></td>
<td><p><span class="math problematic">\vartriangleright</span></p></td>
<td><p><span class="docutils literal">\vartriangleright</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nsubseteq</span></p></td>
<td><p><span class="docutils literal">\nsubseteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sqsubseteq;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sqsubseteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&vdash;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\vdash</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nsubseteqq</span></p></td>
<td><p><span class="docutils literal">\nsubseteqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sqsupset;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sqsupset</span></p></td>
<td><p><span class="math problematic">\Vdash</span></p></td>
<td><p><span class="docutils literal">\Vdash</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nsupseteq</span></p></td>
<td><p><span class="docutils literal">\nsupseteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sqsupseteq;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\sqsupseteq</span></p></td>
<td><p><span class="math problematic">\vDash</span></p></td>
<td><p><span class="docutils literal">\vDash</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\nsupseteqq</span></p></td>
<td><p><span class="docutils literal">\nsupseteqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sub;</mo></mrow></math></p></td>
<td><p><span class="docutils literal">\subset</span></p></td>
<td><p><span class="math problematic">\Vvdash</span></p></td>
<td><p><span class="docutils literal">\Vvdash</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\ntriangleleft</span></p></td>
<td><p><span class="docutils literal">\ntriangleleft</span></p></td>
<td><p><span class="math problematic">\Subset</span></p></td>
<td><p><span class="docutils literal">\Subset</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 570)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \backepsilon in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 570)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ntrianglelefteq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 571)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \because in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 571)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ntriangleright in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \subseteqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \between in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 572)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ntrianglerighteq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 572)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \subsetneq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 573)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \blacktriangleleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 573)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nvdash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 573)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \subsetneqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 574)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \blacktriangleright in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 574)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nVdash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 575)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nvDash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 575)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Supset in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 576)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nVDash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 577)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \supseteqq in equation, Line 1.</p>
</aside>
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<p>TeX to MathML converter `ttm` failed:</p>
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<p>TeX to MathML converter `ttm` failed:</p>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \therefore in equation, Line 1.</p>
</aside>
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<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 581)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \shortmid in equation, Line 1.</p>
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<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \trianglelefteq in equation, Line 1.</p>
</aside>
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<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 582)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nmid in equation, Line 1.</p>
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<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 582)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \shortparallel in equation, Line 1.</p>
</aside>
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<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 582)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \trianglerighteq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 583)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \smallfrown in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 583)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \varpropto in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 584)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nparallel in equation, Line 1.</p>
</aside>
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<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 584)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \smallsmile in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 584)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \vartriangle in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 585)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nshortmid in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 585)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \vartriangleleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 586)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nshortparallel in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 586)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \vartriangleright in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 587)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nsubseteq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 588)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nsubseteqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 588)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Vdash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 589)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nsupseteq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 589)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \vDash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 590)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nsupseteqq in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 590)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Vvdash in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 591)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ntriangleleft in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 591)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \Subset in equation, Line 1.</p>
</aside>
<p>Synonyms: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sup;</mo></mrow></math> <span class="docutils literal">\owns</span>.</p>
<p>Symbols can be negated prepending <span class="docutils literal">\not</span>, e.g.
<span class="math problematic">\not\in</span> <span class="docutils literal">\not\in</span>, <span class="math problematic">\not\ni</span> <span class="docutils literal">\not\ni</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 596)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \not in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 596)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \not in equation, Line 1.</p>
</aside>
<p>The commands <span class="docutils literal">\varsubsetneq</span>, <span class="docutils literal">\varsubsetneqq</span>, <span class="docutils literal">\varsupsetneq</span>,
and <span class="docutils literal">\varsupsetneqq</span> are not supported with MathML output as there is no
corresponding Unicode character.</p>
</section>
</section>
<section id="variable-sized-operators">
<h3><a class="toc-backref" href="#toc-entry-19" role="doc-backlink"><span class="sectnum">2.12 </span>Variable-sized operators</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&sum;</mo></mrow></math>      <span class="docutils literal">\sum</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&Pi;</mo></mrow></math>     <span class="docutils literal">\prod</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigcap;</mo></mrow></math>   <span class="docutils literal">\bigcap</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigodot;</mo></mrow></math>   <span class="docutils literal">\bigodot</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&int;</mo></mrow></math>      <span class="docutils literal">\int</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&coprod;</mo></mrow></math>   <span class="docutils literal">\coprod</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigcup;</mo></mrow></math>   <span class="docutils literal">\bigcup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigoplus;</mo></mrow></math>  <span class="docutils literal">\bigoplus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&oint;</mo></mrow></math>     <span class="docutils literal">\oint</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigwedge;</mo></mrow></math> <span class="docutils literal">\bigwedge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&biguplus;</mo></mrow></math> <span class="docutils literal">\biguplus</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigotimes;</mo></mrow></math> <span class="docutils literal">\bigotimes</span></p></td>
</tr>
<tr><td><p><span class="math problematic">\smallint</span> <span class="docutils literal">\smallint</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigvee;</mo></mrow></math>   <span class="docutils literal">\bigvee</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>&bigsqcup;</mo></mrow></math> <span class="docutils literal">\bigsqcup</span></p></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 612)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \smallint in equation, Line 1.</p>
</aside>
<p>Larger symbols are used in displayed formulas, sum-like symbols have
indices above/below the symbol:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow>
<munderover><mo>&sum;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn> </mrow>
<mrow><mi>N</mi></mrow></munderover>
<msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow>
</msub>
<mi>&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;</mi>
<msubsup><mrow><mo>&int;</mo></mrow><mrow><mn>0</mn> </mrow>
<mrow><mn>1</mn></mrow></msubsup>
<mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>&ensp;</mi><mi mathvariant="italic">dx</mi><mi>&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;</mi>
<munderover><mo>&Pi;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn> </mrow>
<mrow><mn>10</mn></mrow></munderover>
<msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow>
</msub>
<mo>&#x2026;</mo></mrow>
    </mstyle></math>
</div>
</section>
</section>
<section id="notations">
<h2><a class="toc-backref" href="#toc-entry-20" role="doc-backlink"><span class="sectnum">3 </span>Notations</a></h2>
<section id="top-and-bottom-embellishments">
<h3><a class="toc-backref" href="#toc-entry-21" role="doc-backlink"><span class="sectnum">3.1 </span>Top and bottom embellishments</a></h3>
<p>See <a class="reference internal" href="#accents-and-embellishments">Accents and embellishments</a>.</p>
</section>
<section id="extensible-arrows">
<h3><a class="toc-backref" href="#toc-entry-22" role="doc-backlink"><span class="sectnum">3.2 </span>Extensible arrows</a></h3>
<p>xleftarrow and xrightarrow produce arrows that extend automatically to
accommodate unusually wide subscripts or superscripts. These commands
take one optional argument (the subscript) and one mandatory argument
(the superscript, possibly empty):</p>
<pre class="literal-block">A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</pre>
<p>results in</p>
<pre class="math problematic">
A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 644)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \xleftarrow in equation, Line 1.
Unknown command \xrightarrow in equation, Line 1.</p>
</aside>
</section>
<section id="affixing-symbols-to-other-symbols">
<h3><a class="toc-backref" href="#toc-entry-23" role="doc-backlink"><span class="sectnum">3.3 </span>Affixing symbols to other symbols</a></h3>
<p>In addition to the standard <a class="reference internal" href="#accents-and-embellishments">accents and embellishments</a>, other symbols
can be placed above or below a base symbol with the <span class="docutils literal">\overset</span> and
<span class="docutils literal">\underset</span> commands. The symbol is set in &quot;scriptstyle&quot; (smaller font
size). For example, writing <span class="docutils literal"><span class="pre">\overset{*}{X}</span></span> becomes <span class="math problematic">\overset{*}{X}</span>
and <span class="docutils literal"><span class="pre">\underset{+}{M}</span></span> becomes <span class="math problematic">\underset{+}{M}</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 650)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \overset in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 650)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \underset in equation, Line 1.</p>
</aside>
</section>
<section id="matrices">
<h3><a class="toc-backref" href="#toc-entry-24" role="doc-backlink"><span class="sectnum">3.4 </span>Matrices</a></h3>
<p>The <span class="docutils literal">matrix</span> and <span class="docutils literal">cases</span> environments can also contain <span class="docutils literal">\\</span> and
<span class="docutils literal">&amp;</span>:</p>
<pre class="literal-block">.. math::
   \left ( \begin{matrix} a &amp; b \\ c &amp; d \end{matrix}\right)</pre>
<p>Result:</p>
<pre class="math problematic">
\left ( \begin{matrix} a &amp; b \\ c &amp; d \end{matrix} \right)
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 668)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{matrix} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..
Error: Fatal Abnormal eqdepth 2 on display equation exit, line 1.</p>
</aside>
<p>The environments <span class="docutils literal">pmatrix</span>, <span class="docutils literal">bmatrix</span>, <span class="docutils literal">Bmatrix</span>, <span class="docutils literal">vmatrix</span>, and
<span class="docutils literal">Vmatrix</span> have (respectively) ( ), [ ], { }, | |, and <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">&Verbar;</mo><mi>&ensp;</mi><mo stretchy="false">&Verbar;</mo></mrow></math>
delimiters built in, e.g.</p>
<pre class="math problematic">
\begin{pmatrix} a &amp; b \\ c &amp; d \end{pmatrix} \qquad
\begin{bmatrix} a &amp; b \\ c &amp; d \end{bmatrix} \qquad
\begin{Vmatrix} a &amp; b \\ c &amp; d \end{Vmatrix}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 675)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{pmatrix} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..
Unknown or ignored environment: \begin{bmatrix} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..
Unknown or ignored environment: \begin{Vmatrix} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..
Error: Fatal Abnormal eqdepth 2 on display equation exit, line 2.</p>
</aside>
<p>To produce a small matrix suitable for use in text, there is a
<span class="docutils literal">smallmatrix</span> environment
<span class="math problematic">\bigl(\begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix}\bigr)</span>
that comes closer to fitting within a single text line than a normal
matrix.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 679)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{smallmatrix} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..</p>
</aside>
<p>For piecewise function definitions there is a <span class="docutils literal">cases</span> environment:</p>
<pre class="math problematic">
\mathrm{sgn}(x) = \begin{cases}
            -1 &amp; x&lt;0\\
  \phantom{-}1 &amp; x&gt;0
\end{cases}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 688)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{cases} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~2..
Error: Fatal Abnormal eqdepth 2 on display equation exit, line 5.</p>
</aside>
</section>
<section id="spacing-commands">
<h3><a class="toc-backref" href="#toc-entry-25" role="doc-backlink"><span class="sectnum">3.5 </span>Spacing commands</a></h3>
<p>Horizontal spacing of elements can be controlled with the following
commands:</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mi>&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;</mi><mn>4</mn></mrow></math></p></td>
<td></td>
<td><p><span class="docutils literal">3\qquad 4</span></p></td>
<td><p>= 2em</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mi>&emsp;&emsp;&emsp;</mi><mn>4</mn></mrow></math></p></td>
<td></td>
<td><p><span class="docutils literal">3\quad 4</span></p></td>
<td><p>= 1em</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mi>&nbsp;</mi><mn>4</mn></mrow></math></p></td>
<td><p><span class="docutils literal">3~4</span></p></td>
<td><p><span class="docutils literal">3\nobreakspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mi>&ensp;</mi><mn>4</mn></mrow></math></p></td>
<td><p><span class="docutils literal">3\ 4</span></p></td>
<td></td>
<td><p>escaped space</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mi>&ensp;&ensp;</mi><mn>4</mn></mrow></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\;4</span></span></p></td>
<td><p><span class="docutils literal">3\thickspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mi>&ensp;</mi><mn>4</mn></mrow></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\:4</span></span></p></td>
<td><p><span class="docutils literal">3\medspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mi>&ensp;</mi><mn>4</mn></mrow></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\,4</span></span></p></td>
<td><p><span class="docutils literal">3\thinspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mn>4</mn></mrow></math></p></td>
<td><p><span class="docutils literal">3  4</span></p></td>
<td></td>
<td><p>regular space <a class="brackets" href="#footnote-2" id="footnote-reference-6" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn><mn>4</mn></mrow></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\!4</span></span></p></td>
<td><p><span class="docutils literal">3\negthinspace 4</span></p></td>
<td><p>negative space <a class="brackets" href="#footnote-3" id="footnote-reference-7" role="doc-noteref"><span class="fn-bracket">[</span>5<span class="fn-bracket">]</span></a></p></td>
</tr>
<tr><td><p><span class="math problematic m">3\negmedspace 4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\negmedspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><span class="math problematic m">3\negthickspace 4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\negthickspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>3</mn>&nbsp;&nbsp;<mn>4</mn></mrow></math></p></td>
<td></td>
<td><p><span class="docutils literal">3\hspace{1ex}4</span></p></td>
<td><p>custom length</p></td>
</tr>
<tr><td><p><span class="math problematic m">3\mspace{20mu}4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\mspace{20mu}4</span></p></td>
<td><p>custom length <a class="brackets" href="#footnote-4" id="footnote-reference-8" role="doc-noteref"><span class="fn-bracket">[</span>6<span class="fn-bracket">]</span></a></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 712)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \negmedspace in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 713)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \negthickspace in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 715)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mspace in equation, Line 1.</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-2" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-6">4</a><span class="fn-bracket">]</span></span>
<p>Whitespace characters are ignored in LaTeX math mode.</p>
</aside>
<aside class="footnote brackets" id="footnote-3" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-7">5</a><span class="fn-bracket">]</span></span>
<p>Negative spacing does not work with MathML (last tested in Firefox 115).</p>
</aside>
<aside class="footnote brackets" id="footnote-4" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-8">6</a><span class="fn-bracket">]</span></span>
<p>In LaTeX, the unit must be 'mu' (1 mu = 1/18em).</p>
</aside>
</aside>
<p>There are also three commands that leave a space equal to the height and
width of its argument. For example <span class="docutils literal">\phantom{XXX}</span> results in space as
wide and high as three X’s:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow>
<mfrac><mrow>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<mo>+</mo><mn>1</mn></mrow>
<mrow><mi mathvariant="italic">XXX</mi><mo>-</mo><mn>1</mn></mrow>
</mfrac>
</mrow>
    </mstyle></math>
</div>
<p>The commands <span class="docutils literal">\hphantom</span> and <span class="docutils literal">\vphantom</span> insert space with the
width or height of the argument. They are not supported with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
MathML.</p>
</section>
<section id="modular-arithmetic-and-modulo-operation">
<h3><a class="toc-backref" href="#toc-entry-26" role="doc-backlink"><span class="sectnum">3.6 </span>Modular arithmetic and modulo operation</a></h3>
<p>The commands <span class="docutils literal">\bmod</span>, <span class="docutils literal">\pmod</span>, <span class="docutils literal">\mod</span>, and <span class="docutils literal">\pod</span> deal with the
special spacing conventions of the “mod” notation. <a class="brackets" href="#footnote-5" id="footnote-reference-9" role="doc-noteref"><span class="fn-bracket">[</span>7<span class="fn-bracket">]</span></a></p>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\bmod</span></p></td>
<td><p><span class="docutils literal">\gcd(n,m \bmod n)</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>gcd</mo><mo stretchy="false">(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>mod</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\pmod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \pmod b</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>x</mi><mo>&equiv;</mo><mi>y</mi><mo>mod</mo><mi>b</mi></mrow></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \mod c</span></p></td>
<td><p><span class="math problematic m">x\equiv y \mod c</span></p></td>
</tr>
<tr><td><p><span class="docutils literal">\pod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \pod d</span></p></td>
<td><p><span class="math problematic m">x\equiv y \pod d</span></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\operatorname{mod}(m,n)</span></span></p></td>
<td><p><span class="math problematic m">\operatorname{mod}(m,n)</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 746)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \mod in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 747)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \pod in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 748)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \operatorname in equation, Line 1.</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-5" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-9">7</a><span class="fn-bracket">]</span></span>
<p>Currently <a class="reference external" href="https://sourceforge.net/p/docutils/feature-requests/93/">not supported</a> by the &quot;HTML&quot; <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> option
of the HTML writer.</p>
</aside>
</aside>
</section>
<section id="roots">
<h3><a class="toc-backref" href="#toc-entry-27" role="doc-backlink"><span class="sectnum">3.7 </span>Roots</a></h3>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\sqrt</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\sqrt{x^2-1}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow>
<msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>-</mo><mn>1</mn></mrow></msqrt></mrow></math></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\sqrt[3n]{x^2-1}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mroot><mrow>
<msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>-</mo><mn>1</mn></mrow><mrow><mn>3</mn><mi>n</mi></mrow></mroot></mrow></math></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\sqrt\frac{1}{2}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mn>2</mn></mrow>
</mfrac>
</mrow></msqrt></mrow></math></p></td>
</tr>
</tbody>
</table>
</section>
<section id="boxed-formulas">
<h3><a class="toc-backref" href="#toc-entry-28" role="doc-backlink"><span class="sectnum">3.8 </span>Boxed formulas</a></h3>
<p>The command <span class="docutils literal">\boxed</span> puts a box around its argument:</p>
<pre class="math problematic m">
\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 776)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \boxed in equation, Line 1.</p>
</aside>
</section>
</section>
<section id="fractions-and-related-constructions">
<h2><a class="toc-backref" href="#toc-entry-29" role="doc-backlink"><span class="sectnum">4 </span>Fractions and related constructions</a></h2>
<p>The <span class="docutils literal">\frac</span> command takes two ar guments, numerator and denominator,
and typesets them in normal fraction form. For example, <span class="docutils literal">U = <span class="pre">\frac{R}{I}</span></span>
produces <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>U</mi><mo>=</mo>
<mfrac><mrow><mi>R</mi></mrow>
<mrow><mi>I</mi></mrow>
</mfrac>
</mrow></math>. Use <span class="docutils literal">\dfrac</span> or <span class="docutils literal">\tfrac</span> to
force text style and display style respectively.</p>
<pre class="math problematic m">
\frac{x+1}{x-1}  \quad
\dfrac{x+1}{x-1} \quad
\tfrac{x+1}{x-1}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 787)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \dfrac in equation, Line 1.
Unknown command \tfrac in equation, Line 1.</p>
</aside>
<p>and in text: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow>
<mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow>
</mfrac>
</mrow></math>, <span class="math problematic m">\dfrac{x+1}{x-1}</span>, <span class="math problematic m">\tfrac{x+1}{x-1}</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 791)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \dfrac in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 791)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \tfrac in equation, Line 1.</p>
</aside>
<p>For binomial expressions such as <span class="math problematic m">\binom{n}{k}</span>,
there are <span class="docutils literal">\binom</span>, <span class="docutils literal">\dbinom</span> and <span class="docutils literal">\tbinom</span> commands:</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 793)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \binom in equation, Line 1.</p>
</aside>
<pre class="literal-block">2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}</pre>
<p>prints</p>
<pre class="math problematic m">
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 800)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \binom in equation, Line 1.
Unknown command \binom in equation, Line 1.</p>
</aside>
<p>The <span class="docutils literal">\cfrac</span> command for continued fractions uses displaystyle and
padding for sub-fractions:</p>
<pre class="math problematic m">
\frac{\pi}{4} = 1 + \cfrac{1^2}{
                    2 + \cfrac{3^2}{
                        2 + \cfrac{5^2}{
                            2 + \cfrac{7^2}{2 + \cdots}
                    }}}
\qquad \text{vs.}\qquad
\frac{\pi}{4} = 1 + \frac{1^2}{
                    2 + \frac{3^2}{
                        2 + \frac{5^2}{
                            2 + \frac{7^2}{2 + \cdots}
                    }}}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 805)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \cfrac in equation, Line 1.
Unknown command \cfrac in equation, Line 1.
Unknown command \cfrac in equation, Line 1.
Unknown command \cfrac in equation, Line 1.</p>
</aside>
<p>The optional argument <span class="docutils literal">[l]</span> or <span class="docutils literal">[r]</span> for left or right placement of
the numerator is <a class="reference external" href="https://github.com/w3c/mathml/issues/30">not supported by MathML Core</a>:</p>
<pre class="math problematic m">
\cfrac[l]{x}{x-1} \quad
\cfrac{x}{x-1}    \quad
\cfrac[r]{x}{x-1}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 820)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \cfrac in equation, Line 1.
Unknown command \cfrac in equation, Line 1.
Unknown command \cfrac in equation, Line 1.</p>
</aside>
</section>
<section id="delimiter-sizes">
<h2><a class="toc-backref" href="#toc-entry-30" role="doc-backlink"><span class="sectnum">5 </span>Delimiter sizes</a></h2>
<p>Besides the automatic scaling of <a class="reference internal" href="#extensible-delimiters">extensible delimiters</a> with <span class="docutils literal">\left</span>
and <span class="docutils literal">\right</span>, there are four commands to manually select delimiters of
fixed size:</p>
<table>
<tbody>
<tr><td><p>Sizing</p></td>
<td><p>no</p></td>
<td><p><span class="docutils literal">\left</span></p></td>
<td><p><span class="docutils literal">\bigl</span></p></td>
<td><p><span class="docutils literal">\Bigl</span></p></td>
<td><p><span class="docutils literal">\biggl</span></p></td>
<td><p><span class="docutils literal">\Biggl</span></p></td>
</tr>
<tr><td><p>command</p></td>
<td></td>
<td><p><span class="docutils literal">\right</span></p></td>
<td><p><span class="docutils literal">\bigr</span></p></td>
<td><p><span class="docutils literal">\Bigr</span></p></td>
<td><p><span class="docutils literal">\biggr</span></p></td>
<td><p><span class="docutils literal">\Biggr</span></p></td>
</tr>
<tr><td><p>Result</p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo>
<mfrac><mrow><mi>c</mi></mrow>
<mrow><mi>d</mi></mrow>
</mfrac>
<mo stretchy="false">)</mo></mrow></math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mrow><mo>(</mo>
<mfrac><mrow><mi>c</mi></mrow>
<mrow><mi>d</mi></mrow>
</mfrac>
<mo>)</mo></mrow></mrow></math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mo> </mo><mo>(</mo></mrow><mi>b</mi><mrow><mo> </mo><mo>)</mo></mrow><mrow><mo> </mo><mo>(</mo></mrow>
<mfrac><mrow><mi>c</mi></mrow>
<mrow><mi>d</mi></mrow>
</mfrac>
<mrow><mo> </mo><mo>)</mo></mrow></mrow></math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mo> </mo><mo>(</mo></mrow><mi>b</mi><mrow><mo> </mo><mo>)</mo></mrow><mrow><mo> </mo><mo>(</mo></mrow>
<mfrac><mrow><mi>c</mi></mrow>
<mrow><mi>d</mi></mrow>
</mfrac>
<mrow><mo> </mo><mo>)</mo></mrow></mrow></math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mo> </mo><mo>(</mo></mrow><mi>b</mi><mrow><mo> </mo><mo>)</mo></mrow><mrow><mo> </mo><mo>(</mo></mrow>
<mfrac><mrow><mi>c</mi></mrow>
<mrow><mi>d</mi></mrow>
</mfrac>
<mrow><mo> </mo><mo>)</mo></mrow></mrow></math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mo> </mo><mo>(</mo></mrow><mi>b</mi><mrow><mo> </mo><mo>)</mo></mrow><mrow><mo> </mo><mo>(</mo></mrow>
<mfrac><mrow><mi>c</mi></mrow>
<mrow><mi>d</mi></mrow>
</mfrac>
<mrow><mo> </mo><mo>)</mo></mrow></mrow></math></p></td>
</tr>
</tbody>
</table>
<p>There are two or three situations where the delimiter size is commonly
adjusted using these commands:</p>
<p>The first kind of adjustment is done for cumulative operators with
limits, such as summation signs. With <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> the
delimiters usually turn out larger than necessary, and using the <span class="docutils literal">Big</span>
or <span class="docutils literal">bigg</span> sizes instead gives better results:</p>
<pre class="math problematic m">
\left[\sum_i a_i\left\lvert\sum_j x_{ij}\right\rvert^p\right]^{1/p}
\text{ versus }
\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 854)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \lvert in equation, Line 1.
Unknown command \rvert in equation, Line 1.
Unknown command \lvert in equation, Line 1.
Unknown command \rvert in equation, Line 1.</p>
</aside>
<p>The second kind of situation is clustered pairs of delimiters, where
left and right make them all the same size (because that is adequate to
cover the encompassed material), but what you really want is to make some
of the delimiters slightly larger to make the nesting easier to see.</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow><mrow><mo>(</mo><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mo>)</mo></mrow><mrow><mo>(</mo><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mo>)</mo></mrow><mi>&emsp;&emsp;&emsp;</mi>
<mtext>versus</mtext>
<mi>&emsp;&emsp;&emsp;</mi><mrow><mo> </mo><mo>(</mo></mrow><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mrow><mo> </mo><mo>)</mo></mrow><mrow><mo> </mo><mo>(</mo></mrow><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo>
<msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow>
</msub>

<msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow>
</msub>
<mo stretchy="false">)</mo><mrow><mo> </mo><mo>)</mo></mrow></mrow>
    </mstyle></math>
</div>
<p>The third kind of situation is a slightly oversize object in running
text, such as <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mo>|</mo>
<mfrac><mrow><mi>b</mi><mo>'</mo></mrow>
<mrow><mi>d</mi><mo>'</mo></mrow>
</mfrac>
<mo>|</mo></mrow></mrow></math> where the delimiters produced
by <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> cause too much line spreading. <a class="brackets" href="#footnote-6" id="footnote-reference-10" role="doc-noteref"><span class="fn-bracket">[</span>8<span class="fn-bracket">]</span></a> In that case
<span class="docutils literal">\bigl</span> and <span class="docutils literal">\bigr</span> can be used to produce delimiters that are larger
than the base size but still able to fit within the normal line spacing:
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mrow><mo> </mo><mo>|</mo></mrow>
<mfrac><mrow><mi>b</mi><mo>'</mo></mrow>
<mrow><mi>d</mi><mo>'</mo></mrow>
</mfrac>
<mrow><mo> </mo><mo>|</mo></mrow></mrow></math>.</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-6" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-10">8</a><span class="fn-bracket">]</span></span>
<p>With MathML, an example would be parentheses
around a <span class="docutils literal">smallmatrix</span> environment
<span class="math problematic m">\left(\begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix}\right)</span>
vs. <span class="math problematic m">\Bigl(\begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix}\Bigr)</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 877)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{smallmatrix} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 877)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{smallmatrix} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..</p>
</aside>
</aside>
</aside>
</section>
<section id="text">
<h2><a class="toc-backref" href="#toc-entry-31" role="doc-backlink"><span class="sectnum">6 </span>Text</a></h2>
<p>The main use of the command <span class="docutils literal">\text</span> is for words or phrases in a
display. It is similar to <span class="docutils literal">\mbox</span> in its effects but, unlike <span class="docutils literal">\mbox</span>,
automatically produces subscript-size text if used in a subscript,
<span class="docutils literal"><span class="pre">k_{\text{B}}T</span></span> becomes <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<msub><mrow><mi>k</mi></mrow><mrow>
<mtext>B</mtext>
</mrow>
</msub>
<mi>T</mi></mrow></math>.</p>
<p>Whitespace is kept inside the argument:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow>
<msub><mrow><mi>f</mi></mrow><mrow><mo stretchy="false">[</mo>
<msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow>
</msub>
<mo>,</mo>
<msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow>
</msub>
<mo stretchy="false">]</mo></mrow>
</msub>

<mtext> is monotonic for </mtext>
<mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mi>&ensp;</mi><mo>&#x2026;</mo><mo>,</mo><mi>&ensp;</mi><mi>c</mi><mo>+</mo><mn>1</mn></mrow>
    </mstyle></math>
</div>
<p>The text may contain math commands wrapped in <span class="docutils literal">$</span> signs, e.g.</p>
<pre class="math problematic m">
(-1)^{n_i} = \begin{cases} -1 \quad \text{if $n_i$ is odd,} \\
              +1 \quad \text{if $n_i$ is even.}
\end{cases}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 898)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown or ignored environment: \begin{cases} Line 1.
Improper \\ or \cr outside array environment ignored, Line ~1..</p>
</aside>
<!-- TODO ignore {}, handle text-mode commands -->
</section>
<section id="integrals-and-sums">
<h2><a class="toc-backref" href="#toc-entry-32" role="doc-backlink"><span class="sectnum">7 </span>Integrals and sums</a></h2>
<p>The limits on integrals, sums, and similar symbols are placed either to
the side of or above and below the base symbol, depending on convention
and context. In inline formulas and fractions, the limits on sums, and
similar symbols like</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow>
<munder><mo>lim</mo><mrow><mi>n</mi><mo>&rarr;</mo><mi mathvariant="italic">&infin;</mi></mrow>
</munder>

<munderover><mo>&sum;</mo><mrow><mn>1</mn> </mrow>
<mrow><mi>n</mi></mrow></munderover>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mi>n</mi></mrow>
</mfrac>
</mrow>
    </mstyle></math>
</div>
<p>move to index positions: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<munder><mo>lim</mo><mrow><mi>n</mi><mo>&rarr;</mo><mi mathvariant="italic">&infin;</mi></mrow>
</munder>

<munderover><mo>&sum;</mo><mrow><mn>1</mn> </mrow>
<mrow><mi>n</mi></mrow></munderover>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mi>n</mi></mrow>
</mfrac>
</mrow></math>.</p>
<section id="altering-the-placement-of-limits">
<h3><a class="toc-backref" href="#toc-entry-33" role="doc-backlink"><span class="sectnum">7.1 </span>Altering the placement of limits</a></h3>
<p>The commands <span class="docutils literal">\intop</span> and <span class="docutils literal">\ointop</span> produce integral signs with
limits as in sums and similar: <span class="math problematic m">\intop_0^1</span>, <span class="math problematic m">\ointop_c</span> and</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 921)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \intop in equation, Line 1.</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 921)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \ointop in equation, Line 1.</p>
</aside>
<pre class="math problematic m">
\intop_0^1 \quad \ointop_c
   \quad \text{vs.} \quad
\int^1_0   \quad \oint_c
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 924)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \intop in equation, Line 1.
Unknown command \ointop in equation, Line 1.</p>
</aside>
<p>The commands <span class="docutils literal">\limits</span> and <span class="docutils literal">\nolimits</span> override the default placement
of the limits for any operator; <span class="docutils literal">\displaylimits</span> forces standard
positioning as for the sum command. They should follow immediately after
the operator to which they apply.</p>
<p>Compare the same term with default positions, <span class="docutils literal">\limits</span>, and
<span class="docutils literal">\nolimits</span> in inline and display mode: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<munder><mo>lim</mo><mrow><mi>x</mi><mo>&rarr;</mo><mn>0</mn></mrow>
</munder>
<mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></math>,
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<munder><mo>lim</mo><mrow><mi>x</mi><mo>&rarr;</mo><mn>0</mn></mrow>
</munder>
<mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></math>, <span class="math problematic m">\lim\nolimits_{x\to0}f(x)</span>, vs.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 933)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nolimits in equation, Line 1.</p>
</aside>
<pre class="math problematic m">
\lim_{x\to0}f(x), \quad
\lim\limits_{x\to0}f(x) \quad
\lim\nolimits_{x\to0}f(x).
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 937)</p>
<p>TeX to MathML converter `ttm` failed:</p>
<p class="pre-wrap">Unknown command \nolimits in equation, Line 1.</p>
</aside>
<!-- TODO: \substack -->
<!-- TODO: \sideset -->
</section>
</section>
<section id="changing-the-size-of-elements-in-a-formula">
<h2><a class="toc-backref" href="#toc-entry-34" role="doc-backlink"><span class="sectnum">8 </span>Changing the size of elements in a formula</a></h2>
<p>The declarations <a class="brackets" href="#footnote-7" id="footnote-reference-11" role="doc-noteref"><span class="fn-bracket">[</span>9<span class="fn-bracket">]</span></a> <span class="docutils literal">\displaystyle</span>, <span class="docutils literal">\textstyle</span>,
<span class="docutils literal">\scriptstyle</span>, and <span class="docutils literal">\scriptscriptstyle</span>, select a symbol size and
spacing that would be applied in display math, inline
math, first-order subscript, or second-order subscript, respectively
even when the current context would normally yield some other size.</p>
<p>For example <span class="docutils literal"><span class="pre">:math:`\displaystyle</span> <span class="pre">\sum_{n=0}^\infty</span> <span class="pre">\frac{1}{n}`</span></span> is printed as <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<munderover><mo>&sum;</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn> </mrow>
<mrow><mi mathvariant="italic">&infin;</mi></mrow></munderover>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mi>n</mi></mrow>
</mfrac>
</mrow></math>
rather than <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<munderover><mo>&sum;</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn> </mrow>
<mrow><mi mathvariant="italic">&infin;</mi></mrow></munderover>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mi>n</mi></mrow>
</mfrac>
</mrow></math> and</p>
<pre class="literal-block">\frac{\scriptstyle\sum_{n &gt; 0} z^n}
{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}</pre>
<p>yields</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow>
<mfrac><mrow>
<munder><mo>&sum;</mo><mrow><mi>n</mi><mo>&gt;</mo><mn>0</mn></mrow>
</munder>

<msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow>
</msup>
</mrow>
<mrow>
<munder><mo>&Pi;</mo><mrow><mn>1</mn><mo>&le;</mo><mi>k</mi><mo>&le;</mo><mi>n</mi></mrow>
</munder>
<mo stretchy="false">(</mo><mn>1</mn><mo>-</mo>
<msup><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow>
</msup>
<mo stretchy="false">)</mo></mrow>
</mfrac>

<mtext> instead of the default </mtext>

<mfrac><mrow>
<munder><mo>&sum;</mo><mrow><mi>n</mi><mo>&gt;</mo><mn>0</mn></mrow>
</munder>

<msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow>
</msup>
</mrow>
<mrow>
<munder><mo>&Pi;</mo><mrow><mn>1</mn><mo>&le;</mo><mi>k</mi><mo>&le;</mo><mi>n</mi></mrow>
</munder>
<mo stretchy="false">(</mo><mn>1</mn><mo>-</mo>
<msup><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow>
</msup>
<mo stretchy="false">)</mo></mrow>
</mfrac>
<mo>.</mo></mrow>
    </mstyle></math>
</div>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-7" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-11">9</a><span class="fn-bracket">]</span></span>
<p>&quot;Declarations&quot; are commands that affect processing of the current
&quot;group&quot;. In particular, notice where the braces fall that delimit the
effect of the command: Right: <span class="docutils literal">{\displaystyle <span class="pre">...}</span></span> Wrong:
<span class="docutils literal"><span class="pre">\displaystyle{...}</span></span>.</p>
<p>With <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> MathML, the declaration must be the first element
after the opening bracket.</p>
</aside>
</aside>
<div role="list" class="citation-list">
<div class="citation" id="iso-80000-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#citation-reference-1">ISO-80000-2</a><span class="fn-bracket">]</span></span>
<p><cite>Quantities and units – Part 2: Mathematical signs
and symbols to be used in the natural sciences and technology</cite>:
<a class="reference external" href="http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887">http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887</a>.</p>
</div>
</div>
</section>
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